Статті в журналах: "Stochastic Newton algorithms"

1

Kovacevic, Ivana, Branko Kovacevic, and Zeljko Djurovic. "On strong consistency of a class of recursive stochastic Newton-Raphson type algorithms with application to robust linear dynamic system identification." Facta universitatis - series: Electronics and Energetics 21, no. 1 (2008): 1–21. http://dx.doi.org/10.2298/fuee0801001k.

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The recursive stochastic algorithms for estimating the parameters of linear discrete-time dynamic systems in the presence of disturbance uncertainty has been considered in the paper. Problems related to the construction of min-max optimal recursive algorithms are demonstrated. In addition, the robustness of the proposed algorithms has been addressed. Since the min-max optimal solution cannot be achieved in practice, an approximate optimal solution based on a recursive stochastic Newton-Raphson type procedure is suggested. The convergence of the proposed practically applicable robustified recursive algorithm is established theoretically using the martingale theory. Both theoretical and experimental analysis related to the practical robustness of the proposed algorithm are also included. .

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2

Yousefi, Mahsa, and Ángeles Martínez. "Deep Neural Networks Training by Stochastic Quasi-Newton Trust-Region Methods." Algorithms 16, no. 10 (October 20, 2023): 490. http://dx.doi.org/10.3390/a16100490.

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While first-order methods are popular for solving optimization problems arising in deep learning, they come with some acute deficiencies. To overcome these shortcomings, there has been recent interest in introducing second-order information through quasi-Newton methods that are able to construct Hessian approximations using only gradient information. In this work, we study the performance of stochastic quasi-Newton algorithms for training deep neural networks. We consider two well-known quasi-Newton updates, the limited-memory Broyden–Fletcher–Goldfarb–Shanno (BFGS) and the symmetric rank one (SR1). This study fills a gap concerning the real performance of both updates in the minibatch setting and analyzes whether more efficient training can be obtained when using the more robust BFGS update or the cheaper SR1 formula, which—allowing for indefinite Hessian approximations—can potentially help to better navigate the pathological saddle points present in the non-convex loss functions found in deep learning. We present and discuss the results of an extensive experimental study that includes many aspects affecting performance, like batch normalization, the network architecture, the limited memory parameter or the batch size. Our results show that stochastic quasi-Newton algorithms are efficient and, in some instances, able to outperform the well-known first-order Adam optimizer, run with the optimal combination of its numerous hyperparameters, and the stochastic second-order trust-region STORM algorithm.

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3

Forneron, Jean-Jacques, and Serena Ng. "Estimation and Inference by Stochastic Optimization: Three Examples." AEA Papers and Proceedings 111 (May 1, 2021): 626–30. http://dx.doi.org/10.1257/pandp.20211038.

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This paper illustrates two algorithms designed in Forneron and Ng (2020): the resampled Newton-Raphson (rNR) and resampled quasi-Newton (rQN) algorithms, which speed up estimation and bootstrap inference for structural models. An empirical application to BLP shows that computation time decreases from nearly five hours with the standard bootstrap to just over one hour with rNR and to only 15 minutes using rQN. A first Monte Carlo exercise illustrates the accuracy of the method for estimation and inference in a probit IV regression. A second exercise additionally illustrates statistical efficiency gains relative to standard estimation for simulation-based estimation using a dynamic panel regression example.

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4

Cao, Pengfei, and Xionglin Luo. "Performance analysis of multi-innovation stochastic Newton recursive algorithms." Digital Signal Processing 56 (September 2016): 15–23. http://dx.doi.org/10.1016/j.dsp.2016.05.005.

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5

Ghoshdastidar, Debarghya, Ambedkar Dukkipati, and Shalabh Bhatnagar. "Newton-based stochastic optimization using q-Gaussian smoothed functional algorithms." Automatica 50, no. 10 (October 2014): 2606–14. http://dx.doi.org/10.1016/j.automatica.2014.08.021.

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6

Shao, Wei, and Guangbao Guo. "Multiple-Try Simulated Annealing Algorithm for Global Optimization." Mathematical Problems in Engineering 2018 (July 17, 2018): 1–11. http://dx.doi.org/10.1155/2018/9248318.

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Simulated annealing is a widely used algorithm for the computation of global optimization problems in computational chemistry and industrial engineering. However, global optimum values cannot always be reached by simulated annealing without a logarithmic cooling schedule. In this study, we propose a new stochastic optimization algorithm, i.e., simulated annealing based on the multiple-try Metropolis method, which combines simulated annealing and the multiple-try Metropolis algorithm. The proposed algorithm functions with a rapidly decreasing schedule, while guaranteeing global optimum values. Simulated and real data experiments including a mixture normal model and nonlinear Bayesian model indicate that the proposed algorithm can significantly outperform other approximated algorithms, including simulated annealing and the quasi-Newton method.

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7

Gao, Guohua, Gaoming Li, and Albert Coburn Reynolds. "A Stochastic Optimization Algorithm for Automatic History Matching." SPE Journal 12, no. 02 (June 1, 2007): 196–208. http://dx.doi.org/10.2118/90065-pa.

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Summary For large- scale history- matching problems, optimization algorithms which require only the gradient of the objective function and avoid explicit computation of the Hessian appear to be the best approach. Unfortunately, such algorithms have not been extensively used in practice because computation of the gradient of the objective function by the adjoint method requires explicit knowledge of the simulator numerics and expertise in simulation development. Here we apply the simultaneous perturbation stochastic approximation (SPSA) method to history match multiphase flow production data. SPSA, which has recently attracted considerable international attention in a variety of disciplines, can be easily combined with any reservoir simulator to do automatic history matching. The SPSA method uses stochastic simultaneous perturbation of all parameters to generate a down hill search direction at each iteration. The theoretical basis for this probabilistic perturbation is that the expectation of the search direction generated is the steepest descent direction. We present modifications for improvement in the convergence behavior of the SPSA algorithm for history matching and compare its performance to the steepest descent, gradual deformation and LBFGS algorithm. Although the convergence properties of the SPSA algorithm are not nearly as good as our most recent implementation of a quasi-Newton method (LBFGS), the SPSA algorithm is not simulator specific and it requires only a few hours of work to combine SPSA with any commercial reservoir simulator to do automatic history matching. To the best of our knowledge, this is the first introduction of SPSA into the history matching literature. Thus, we make considerable effort to put it in a proper context.

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8

Wang, Qing, and Yang Cao. "Stochastic Finite Element Method for Nonlinear Dynamic Problem with Random Parameters." Advanced Materials Research 189-193 (February 2011): 1348–57. http://dx.doi.org/10.4028/www.scientific.net/amr.189-193.1348.

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Several algorithms were proposed relating to the development of a framework of the perturbation-based stochastic finite element method (PSFEM) for nonlinear dynamic problem with random parameters, for this purpose, based on the stochastic virtual work principle , some algorithms and a framework related to SFEM have been studied. An interpolation method was used to discretize the random fields, which is based on representing the random field in terms of an interpolation rule involving a set of deterministic shape functions. Direct integration Wilson- Method in conjunction with Newton-Raphson scheme was adopted to solve finite element equations. Numerical examples were compared with Monte-Carlo simulation method to show that the approaches proposed herein are accurate and effective for the nonlinear dynamic analysis of structures with random parameters

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9

Wang, Yanshan, In-Chan Choi, and Hongfang Liu. "Generalized ensemble model for document ranking in information retrieval." Computer Science and Information Systems 14, no. 1 (2017): 123–51. http://dx.doi.org/10.2298/csis160229042w.

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A generalized ensemble model (gEnM) for document ranking is proposed in this paper. The gEnM linearly combines the document retrieval models and tries to retrieve relevant documents at high positions. In order to obtain the optimal linear combination of multiple document retrieval models or rankers, an optimization program is formulated by directly maximizing the mean average precision. Both supervised and unsupervised learning algorithms are presented to solve this program. For the supervised scheme, two approaches are considered based on the data setting, namely batch and online setting. In the batch setting, we propose a revised Newton?s algorithm, gEnM.BAT, by approximating the derivative and Hessian matrix. In the online setting, we advocate a stochastic gradient descent (SGD) based algorithm-gEnM.ON. As for the unsupervised scheme, an unsupervised ensemble model (UnsEnM) by iteratively co-learning from each constituent ranker is presented. Experimental study on benchmark data sets verifies the effectiveness of the proposed algorithms. Therefore, with appropriate algorithms, the gEnM is a viable option in diverse practical information retrieval applications.

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10

Clayton, R. P., and R. F. Martinez-Botas. "Application of generic algorithms in aerodynamic optimisation design procedures." Aeronautical Journal 108, no. 1090 (December 2004): 611–20. http://dx.doi.org/10.1017/s0001924000000440.

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AbstractDirect optimisation techniques using different methods are presented and compared for the solution of two common flows: a two dimensional diffuser and a drag minimisation problem of a fixed area body. The methods studied are a truncated Newton algorithm (gradient method), a simplex approach (direct search method) and a genetic algorithm (stochastic method). The diffuser problem has a known solution supported by experimental data, it has one design performance measure (the pressure coefficient) and two design variables. The fixed area body also has one performance measure (the drag coefficient), but this time there are four design variables; no experimental data is available, this computation is performed to assess the speed/progression of solution.In all cases the direct search approach (simplex method) required significantly smaller number of evaluations than the generic algorithm method. The simplest approach, the gradient method (Newton) performed equally to the simplex approach for the diffuser problem but it was unable to provide a solution to the four-variable problem of a fixed area body drag minimisation. The level of robustness obtained by the use of generic algorithm is in principle superior to the other methods, but a large price in terms of evaluations has to be paid.

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11

Incorvaia, Gabriele, and Oliver Dorn. "Stochastic Optimization Methods for Parametric Level Set Reconstructions in 2D through-the-Wall Radar Imaging." Electronics 9, no. 12 (December 3, 2020): 2055. http://dx.doi.org/10.3390/electronics9122055.

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In this paper, a comparison of stochastic optimization algorithms is presented for the reconstruction of electromagnetic profiles in through-the-wall radar imaging. We combine those stochastic optimization approaches with a shape-based representation of unknown targets which is based on a parametrized level set formulation. This way, we obtain a stochastic version of shape evolution with the goal of minimizing a given cost functional. As basis functions, we consider in particular Gaussian and Wendland radial basis functions. For the optimization task, we consider three variants of stochastic approaches, namely stochastic gradient descent, the Adam method as well as a more involved stochastic quasi-Newton scheme. A specific backtracking line search method is also introduced for this specific application of stochastic shape evolution. The physical scenery considered here is set in 2D assuming TM waves for simplicity. The goal is to localize and characterize (and eventually track) targets of interest hidden behind walls by solving the corresponding electromagnetic inverse problem. The results provide a good indication on the expected performance of similar schemes in a more realistic 3D setup.

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12

Charalambous, C. D., and J. L. Hibey. "Exact filters for Newton–Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems." Systems & Control Letters 42, no. 2 (February 2001): 101–15. http://dx.doi.org/10.1016/s0167-6911(00)00082-7.

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13

Sochi, Taha. "Deterministic and stochastic algorithms for resolving the flow fields in ducts and networks using energy minimization." International Journal of Modern Physics C 27, no. 04 (February 23, 2016): 1650036. http://dx.doi.org/10.1142/s0129183116500364.

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Several deterministic and stochastic multi-variable global optimization algorithms (Conjugate Gradient, Nelder–Mead, Quasi-Newton and global) are investigated in conjunction with energy minimization principle to resolve the pressure and volumetric flow rate fields in single ducts and networks of interconnected ducts. The algorithms are tested with seven types of fluid: Newtonian, power law, Bingham, Herschel–Bulkley, Ellis, Ree–Eyring and Casson. The results obtained from all those algorithms for all these types of fluid agree very well with the analytically derived solutions as obtained from the traditional methods which are based on the conservation principles and fluid constitutive relations. The results confirm and generalize the findings of our previous investigations that the energy minimization principle is at the heart of the flow dynamics systems. The investigation also enriches the methods of computational fluid dynamics for solving the flow fields in tubes and networks for various types of Newtonian and non-Newtonian fluids.

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14

Isabona, Joseph, Agbotiname Lucky Imoize, Oluwasayo Akinloye Akinwumi, Okiemute Roberts Omasheye, Emughedi Oghu, Cheng-Chi Lee, and Chun-Ta Li. "Optimal Radio Propagation Modeling and Parametric Tuning Using Optimization Algorithms." Information 14, no. 11 (November 19, 2023): 621. http://dx.doi.org/10.3390/info14110621.

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Benchmarking different optimization algorithms is tasky, particularly for network-based cellular communication systems. The design and management process of these systems involves many stochastic variables and complex design parameters that demand an unbiased estimation and analysis. Though several optimization algorithms exist for different parametric modeling and tuning, an in-depth evaluation of their functional performance has not been adequately addressed, especially for cellular communication systems. Firstly, in this paper, nine key numerical and global optimization algorithms, comprising Gauss–Newton (GN), gradient descent (GD), Genetic Algorithm (GA), Levenberg–Marguardt (LM), Quasi-Newton (QN), Trust-Region–Dog-Leg (TR), pattern search (PAS), Simulated Annealing (SA), and particle swam (PS), have been benchmarked against measured data. The experimental data were taken from different radio signal propagation terrains around four eNodeB cells. In order to assist the radio frequency (RF) engineer in selecting the most suitable optimization method for the parametric model tuning, three-fold benchmarking criteria comprising the Accuracy Profile Benchmark (APB), Function Evaluation Benchmark (FEB), and Execution Speed Benchmark (ESB) were employed. The APB and FEB were quantitatively compared against the measured data for fair benchmarking. By leveraging the APB performance criteria, the QN achieved the best results with the preferred values of 98.34, 97.31, 97.44, and 96.65% in locations 1–4. The GD attained the worst performance with the lowest APE values of 98.25, 95.45, 96.10, and 95.70 in the tested locations. In terms of objective function values and their evaluation count, the QN algorithm shows the fewest function counts of 44, 44, 56, and 44, and the lowest objective values of 80.85, 37.77, 54.69, and 41.24, thus attaining the best optimization algorithm results across the study locations. The worst performance was attained by the GD with objective values of 86.45, 39.58, 76.66, and 54.27, respectively. Though the objective values achieved with global optimization methods, PAS, GA, PS, and SA, are relatively small compared to the QN, their function evaluation counts are high. The PAS, GA, PS, and SA recorded 1367, 2550, 3450, and 2818 function evaluation counts, which are relatively high. Overall, the QN algorithm achieves the best optimization, and it can serve as a reference for RF engineers in selecting suitable optimization methods for propagation modeling and parametric tuning.

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15

Goryainov, V. B., and W. M. Khing. "Comparison of Classical and Robust Estimates of Threshold Auto-regression Parameters." Mathematics and Mathematical Modeling, no. 5 (February 6, 2021): 33–44. http://dx.doi.org/10.24108/mathm.0520.0000224.

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The exponential auto-regression model is a discrete analog of the second-order nonlinear differential equations of the type of Duffing and van der Pol oscillators. It is used to describe nonlinear stochastic processes with discrete time, such as vehicle vibrations, ship roll, electrical signals in the cerebral cortex. When applying the model in practice, one of the important tasks is its identification, in particular, an estimate of the model parameters from observations of the stochastic process it described. A traditional technique to estimate autoregressive parameters is the nonlinear least squares method. Its disadvantage is high sensitivity to the measurement errors of the process observed. The M-estimate method largely has no such a drawback. The M-estimates are based on the minimization procedure of a non-convex function of several variables. The paper studies the effectiveness of several well-known minimization methods to find the M-estimates of the parameters of an exponential autoregressive model. The paper demonstrates that the sequential quadratic programming algorithm, the active set algorithm, and the interior-point algorithm have shown the best and approximately the same accuracy. The quasi-Newton algorithm is inferior to them in accuracy a little bit, but is not inferior in time. These algorithms had approximately the same speed and were one and a half times faster than the Nelder-Mead algorithm and 14 times faster than the genetic algorithm. The Nelder-Mead algorithm and the genetic algorithm have shown the worst accuracy. It was found that all the algorithms are sensitive to initial conditions. The estimate of parameters, on which the autoregressive equation linearly depends, is by an order of magnitude more accurate than that of the parameter on which the auto-regression equation depends in a nonlinear way.

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16

Ille, Nicole. "Orthogonal extended infomax algorithm." Journal of Neural Engineering 21, no. 2 (April 1, 2024): 026032. http://dx.doi.org/10.1088/1741-2552/ad38db.

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Abstract Objective. The extended infomax algorithm for independent component analysis (ICA) can separate sub- and super-Gaussian signals but converges slowly as it uses stochastic gradient optimization. In this paper, an improved extended infomax algorithm is presented that converges much faster. Approach. Accelerated convergence is achieved by replacing the natural gradient learning rule of extended infomax by a fully-multiplicative orthogonal-group based update scheme of the ICA unmixing matrix, leading to an orthogonal extended infomax algorithm (OgExtInf). The computational performance of OgExtInf was compared with original extended infomax and with two fast ICA algorithms: the popular FastICA and Picard, a preconditioned limited-memory Broyden–Fletcher–Goldfarb–Shanno (L-BFGS) algorithm belonging to the family of quasi-Newton methods. Main results. OgExtInf converges much faster than original extended infomax. For small-size electroencephalogram (EEG) data segments, as used for example in online EEG processing, OgExtInf is also faster than FastICA and Picard. Significance. OgExtInf may be useful for fast and reliable ICA, e.g. in online systems for epileptic spike and seizure detection or brain-computer interfaces.

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17

Huang, Meihua, Pongsakorn Sunthrayuth, Amjad Ali Pasha, and Muhammad Altaf Khan. "Numerical solution of stochastic and fractional competition model in Caputo derivative using Newton method." AIMS Mathematics 7, no. 5 (2022): 8933–52. http://dx.doi.org/10.3934/math.2022498.

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<abstract><p>Many useful numerical algorithms of the numerical solution are proposed due to the increasing interest of the researchers in fractional calculus. A new discretization of the competition model for the real statistical data of banking finance for the years 2004–2014 is presented. We use a novel numerical method that is more reliable and accurate which is introduced recently for the solution of ordinary differential equations numerically. We apply this approach to solve our model for the case of Caputo derivative. We apply the Caputo derivative on the competition system and obtain its numerical results. For the numerical solution of the competition model, we use the Newton polynomial approach and present in detail a novel numerical procedure. We utilize the numerical procedure and present various numerical results in the form of graphics. A comparison of the present method versus the predictor corrector method is presented, which shows the same solution behavior to the Newton Polynomial approach. We also suggest that the real data versus model provide good fitting for both the data for the fractional-order parameter value $ \rho = 0.7 $. Some more values of $ \rho $ are used to obtain graphical results. We also check the model in the stochastic version and show the model behaves well when fitting to the data.</p></abstract>

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18

Roeva, Olympia, and Dafina Zoteva. "Model Identification of E. coli Cultivation Process Applying Hybrid Crow Search Algorithm." Fermentation 10, no. 1 (December 22, 2023): 12. http://dx.doi.org/10.3390/fermentation10010012.

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Cultivation process (CP) modeling and optimization are ambitious tasks due to the nonlinear nature of the models and interdependent parameters. The identification procedures for such models are challenging. Metaheuristic algorithms exhibit promising performance for such complex problems since a near-optimal solution can be found in an acceptable time. The present research explores a new hybrid metaheuristic algorithm built upon the good exploration of the genetic algorithm (GA) and the exploitation of the crow search algorithm (CSA). The efficiency of the proposed GA-CSA hybrid is studied with the model parameter identification procedure of the E. coli BL21(DE3)pPhyt109 fed-batch cultivation process. The results are compared with those of the pure GA and pure CSA applied to the same problem. A comparison with two deterministic algorithms, i.e., sequential quadratic programming (SQP) and the Quasi-Newton (Q-N) method, is also provided. A more accurate model is obtained by the GA-CSA hybrid with fewer computational resources. Although SQP and Q-N find a solution for a smaller number of function evaluations, the resulting models are not as accurate as the models generated by the three metaheuristic algorithms. The InterCriteria analysis, a mathematical approach to revealing certain relations between given criteria, and a series of statistical tests are employed to prove that there is a statistically significant difference between the results of the three stochastic algorithms. The obtained mathematical models are then successfully verified with a different set of experimental data, in which, again, the closest one is the GA-CSA model. The GA-CSA hybrid proposed in this paper is proven to be successful in the collaborative hybridization of GA and CSA with outstanding performance.

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19

Nzokem, Aubain Hilaire. "Pricing European Options under Stochastic Volatility Models: Case of Five-Parameter Variance-Gamma Process." Journal of Risk and Financial Management 16, no. 1 (January 16, 2023): 55. http://dx.doi.org/10.3390/jrfm16010055.

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The paper builds a Variance-Gamma (VG) model with five parameters: location (μ), symmetry (δ), volatility (σ), shape (α), and scale (θ); and studies its application to the pricing of European options. The results of our analysis show that the five-parameter VG model is a stochastic volatility model with a Γ(α,θ) Ornstein–Uhlenbeck type process; the associated Lévy density of the VG model is a KoBoL family of order ν=0, intensity α, and steepness parameters δσ2−δ2σ4+2θσ2 and δσ2+δ2σ4+2θσ2; and the VG process converges asymptotically in distribution to a Lévy process driven by a normal distribution with mean (μ+αθδ) and variance α(θ2δ2+σ2θ). The data used for empirical analysis were obtained by fitting the five-parameter Variance-Gamma (VG) model to the underlying distribution of the daily SPY ETF data. Regarding the application of the five-parameter VG model, the twelve-point rule Composite Newton–Cotes Quadrature and Fractional Fast Fourier (FRFT) algorithms were implemented to compute the European option price. Compared to the Black–Scholes (BS) model, empirical evidence shows that the VG option price is underpriced for out-of-the-money (OTM) options and overpriced for in-the-money (ITM) options. Both models produce almost the same option pricing results for deep out-of-the-money (OTM) and deep-in-the-money (ITM) options.

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20

Ahmed, Essam A., Tariq S. Alshammari, and Mohamed S. Eliwa. "Different Statistical Inference Algorithms for the New Pareto Distribution Based on Type-II Progressively Censored Competing Risk Data with Applications." Mathematics 12, no. 13 (July 7, 2024): 2136. http://dx.doi.org/10.3390/math12132136.

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In this research, the statistical inference of unknown lifetime parameters is proposed in the presence of independent competing risks using a progressive Type-II censored dataset. The lifetime distribution associated with a failure mode is assumed to follow the new Pareto distribution, with consideration given to two distinct competing failure reasons. Maximum likelihood estimators (MLEs) for the unknown model parameters, as well as reliability and hazard functions, are derived, noting that they are not expressible in closed form. The Newton–Raphson, expectation maximization (EM), and stochastic expectation maximization (SEM) methods are employed to generate maximum likelihood (ML) estimations. Approximate confidence intervals for the unknown parameters, reliability, and hazard rate functions are constructed using the normal approximation of the MLEs and the normal approximation of the log-transformed MLEs. Additionally, the missing information principle is utilized to derive the closed form of the Fisher information matrix, which, in turn, is used with the delta approach to calculate confidence intervals for reliability and hazards. Bayes estimators are derived under both symmetric and asymmetric loss functions, with informative and non-informative priors considered, including independent gamma distributions for informative priors. The Monte Carlo Markov Chain sampling approach is employed to obtain the highest posterior density credible intervals and Bayesian point estimates for unknown parameters and reliability characteristics. A Monte Carlo simulation is conducted to assess the effectiveness of the proposed techniques, with the performances of the Bayes and maximum likelihood estimations examined using average values and mean squared errors as benchmarks. Interval estimations are compared in terms of average lengths and coverage probabilities. Real datasets are considered and examined for each topic to provide illustrative examples.

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Ketabchi, Saeed, and Malihe Behboodi-Kahoo. "Smoothing Techniques and Augmented Lagrangian Method for Recourse Problem of Two-Stage Stochastic Linear Programming." Journal of Applied Mathematics 2013 (2013): 1–8. http://dx.doi.org/10.1155/2013/735916.

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The augmented Lagrangian method can be used for solving recourse problems and obtaining their normal solution in solving two-stage stochastic linear programming problems. The augmented Lagrangian objective function of a stochastic linear problem is not twice differentiable which precludes the use of a Newton method. In this paper, we apply the smoothing techniques and a fast Newton-Armijo algorithm for solving an unconstrained smooth reformulation of this problem. Computational results and comparisons are given to show the effectiveness and speed of the algorithm.

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Liu, Hanger, Yan Li, and Maojun Zhang. "An Active Set Limited Memory BFGS Algorithm for Machine Learning." Symmetry 14, no. 2 (February 14, 2022): 378. http://dx.doi.org/10.3390/sym14020378.

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In this paper, a stochastic quasi-Newton algorithm for nonconvex stochastic optimization is presented. It is derived from a classical modified BFGS formula. The update formula can be extended to the framework of limited memory scheme. Numerical experiments on some problems in machine learning are given. The results show that the proposed algorithm has great prospects.

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23

Stephen, Karl D., Juan Soldo, Colin Macbeth, and Mike A. Christie. "Multiple Model Seismic and Production History Matching: A Case Study." SPE Journal 11, no. 04 (December 1, 2006): 418–30. http://dx.doi.org/10.2118/94173-pa.

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Summary Time-lapse (or 4D) seismic is increasingly being used as a qualitative description of reservoir behavior for management and decision-making purposes. When combined quantitatively with geological and flow modeling as part of history matching, improved predictions of reservoir production can be obtained. Here, we apply a method of multiple-model history matching based on simultaneous comparison of spatial data offered by seismic as well as individual well-production data. Using a petroelastic transform and suitable rescaling, forward-modeled simulations are converted into predictions of seismic impedance attributes and compared to observed data by calculation of a misfit. A similar approach is applied to dynamic well data. This approach improves on gradient-based methods by avoiding entrapment in local minima. We demonstrate the method by applying it to the UKCS Schiehallion reservoir, updating the operator's model. We consider a number of parameters to be uncertain. The reservoir's net to gross is initially updated to better match the observed baseline acoustic impedance derived from the RMS amplitudes of the migrated stack. We then history match simultaneously for permeability, fault transmissibility multipliers, and the petroelastic transform parameters. Our results show a good match to the observed seismic and well data with significant improvement to the base case. Introduction Reservoir management requires tools such as simulation models to predict asset behavior. History matching is often employed to alter these models so that they compare favorably to observed well rates and pressures. This well information is obtained at discrete locations and thus lacks the areal coverage necessary to accurately constrain dynamic reservoir parameters such as permeability and the location and effect of faults. Time-lapse seismic captures the effect of pressure and saturation on seismic impedance attributes, giving 2D maps or 3D volumes of the missing information. The process of seismic history matching attempts to overlap the benefits of both types of information to improve estimates of the reservoir model parameters. We first present an automated multiple-model history-matching method that includes time-lapse seismic along with production data, based on an integrated workflow (Fig. 1). It improves on the classical approach, wherein the engineer manually adjusts parameters in the simulation model. Our method also improves on gradient-based methods, such as Steepest Descent, Gauss-Newton, and Levenberg-Marquardt algorithms (e.g., Lépine et al. 1999;Dong and Oliver 2003; Gosselin et al. 2003; Mezghani et al. 2004), which are good at finding local likelihood maxima but can fail to find the global maximum. Our method is also faster than stochastic methods such as genetic algorithms and simulated annealing, which often require more simulations and may have slower convergence rates. Finally, multiple models are generated, enabling posterior uncertainty analysis in a Bayesian framework (as in Stephen and MacBeth 2006a).

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Davila, C. E. "A stochastic Newton algorithm with data-adaptive step size." IEEE Transactions on Acoustics, Speech, and Signal Processing 38, no. 10 (1990): 1796–98. http://dx.doi.org/10.1109/29.60110.

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Li, Heng, Jun Peng, Weirong Liu, Zhiwu Huang, and Kuo-Chi Lin. "A Newton-Based Extremum Seeking MPPT Method for Photovoltaic Systems with Stochastic Perturbations." International Journal of Photoenergy 2014 (2014): 1–13. http://dx.doi.org/10.1155/2014/938526.

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Microcontroller based maximum power point tracking (MPPT) has been the most popular MPPT approach in photovoltaic systems due to its high flexibility and efficiency in different photovoltaic systems. It is well known that PV systems typically operate under a range of uncertain environmental parameters and disturbances, which implies that MPPT controllers generally suffer from some unknown stochastic perturbations. To address this issue, a novel Newton-based stochastic extremum seeking MPPT method is proposed. Treating stochastic perturbations as excitation signals, the proposed MPPT controller has a good tolerance of stochastic perturbations in nature. Different from conventional gradient-based extremum seeking MPPT algorithm, the convergence rate of the proposed controller can be totally user-assignable rather than determined by unknown power map. The stability and convergence of the proposed controller are rigorously proved. We further discuss the effects of partial shading and PV module ageing on the proposed controller. Numerical simulations and experiments are conducted to show the effectiveness of the proposed MPPT algorithm.

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26

Milzarek, Andre, Fabian Schaipp, and Michael Ulbrich. "A Semismooth Newton Stochastic Proximal Point Algorithm with Variance Reduction." SIAM Journal on Optimization 34, no. 1 (March 26, 2024): 1157–85. http://dx.doi.org/10.1137/22m1488181.

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27

Bishwal, Jaya P. N. "MLE Evolution Equation for Fractional Diffusions and Berry-Esseen Inequality of Stochastic Gradient Descent Algorithm for American Option." European Journal of Statistics 2 (September 6, 2022): 13. http://dx.doi.org/10.28924/ada/stat.2.13.

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We study recursive parameter estimation in fractional diffusion processes. First, stability and asymptotic properties of the global maximum likelihood estimator (MLE) of the drift parameter are obtained under some regularity conditions. Then we obtain an evolution equation for the MLE of the drift parameter in nonhomogeneous fractional stochastic differential equation (fSDE) driven by fractional Brownian motion. This equation is then modified to yield an algorithm which is consistent, asymptotically efficient and converges to the MLE. The gradient and Newton type algorithm are firstorder approximations. Finally we study the Berry-Esseen inequality for stochastic gradient descent in continuous time (SGDCT) algorithm for American option. We compare it with Longstaff-Schwartz regression based method.

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28

Bercu, Bernard, Antoine Godichon, and Bruno Portier. "An Efficient Stochastic Newton Algorithm for Parameter Estimation in Logistic Regressions." SIAM Journal on Control and Optimization 58, no. 1 (January 2020): 348–67. http://dx.doi.org/10.1137/19m1261717.

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29

Mazzi, Claudio, Angelo Damone, Andrea Vandelli, Gastone Ciuti, and Milena Vainieri. "Stochastic Claims Reserve in the Healthcare System: A Methodology Applied to Italian Data." Risks 12, no. 2 (January 29, 2024): 24. http://dx.doi.org/10.3390/risks12020024.

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One of the challenges in the healthcare sector is making accurate forecasts across insurance years for claims reserve. Healthcare claims present huge variability and heterogeneity influenced by random decisions of the courts and intrinsic characteristics of the damaged parties, which makes traditional methods for estimating reserves inadequate. We propose a new methodology to estimate claim reserves in the healthcare insurance system based on generalized linear models using the Overdispersed Poisson distribution function. In this context, we developed a method to estimate the parameters of the quasi-likelihood function using a Gauss–Newton algorithm optimized through a genetic algorithm. The genetic algorithm plays a crucial role in glimpsing the position of the global minimum to ensure a correct convergence of the Gauss–Newton method, where the choice of the initial guess is fundamental. This methodology is applied as a case study to the healthcare system of the Tuscany region. The results were validated by comparing them with state-of-the-art measurement of the confidence intervals of the Overdispersed Poisson distribution parameters with better outcomes. Hence, local healthcare authorities could use the proposed and improved methodology to allocate resources dedicated to healthcare and global management.

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30

Sparks, A. G., and D. S. Bernstein. "Optimal Rejection of Stochastic and Deterministic Disturbances." Journal of Dynamic Systems, Measurement, and Control 119, no. 1 (March 1, 1997): 140–43. http://dx.doi.org/10.1115/1.2801207.

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The problem of optimal H2 rejection of noisy disturbances while asymptotically rejecting constant or sinusoidal disturbances is considered. The internal model principle is used to ensure that the expected value of the output approaches zero asymptotically in the presence of persistent deterministic disturbances. Necessary conditions are given for dynamic output feedback controllers that minimize an H2 disturbance rejection cost plus an upper bound on the integral square output cost for transient performance. The necessary conditions provide expressions for the gradients of the cost with respect to each of the control gains. These expressions are then used in a quasi-Newton gradient search algorithm to find the optimal feedback gains.

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31

Chu, Dejun, Changshui Zhang, Shiliang Sun, and Qing Tao. "Structured BFGS Method for Optimal Doubly Stochastic Matrix Approximation." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 6 (June 26, 2023): 7193–201. http://dx.doi.org/10.1609/aaai.v37i6.25877.

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Doubly stochastic matrix plays an essential role in several areas such as statistics and machine learning. In this paper we consider the optimal approximation of a square matrix in the set of doubly stochastic matrices. A structured BFGS method is proposed to solve the dual of the primal problem. The resulting algorithm builds curvature information into the diagonal components of the true Hessian, so that it takes only additional linear cost to obtain the descent direction based on the gradient information without having to explicitly store the inverse Hessian approximation. The cost is substantially fewer than quadratic complexity of the classical BFGS algorithm. Meanwhile, a Newton-based line search method is presented for finding a suitable step size, which in practice uses the existing knowledge and takes only one iteration. The global convergence of our algorithm is established. We verify the advantages of our approach on both synthetic data and real data sets. The experimental results demonstrate that our algorithm outperforms the state-of-the-art solvers and enjoys outstanding scalability.

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32

Liu, Qiang, Rang Ding Wang, Ying Zhu, and Cheng Tou Du. "An Algorithm to Eliminate Stochastic Jump Measurements of Ultrasonic Flow-Meter with Time Difference Method." Advanced Materials Research 267 (June 2011): 414–21. http://dx.doi.org/10.4028/www.scientific.net/amr.267.414.

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This article describes the time difference ultrasonic flow meter measurement principle, by analyzing the ultrasonic flow meter test results, using the theory of Newton interpolation correction calibration constants, solves the problems that the measurement results will suddenly appear more random beating and further improve measurement accuracy of the ultrasonic flow meter.

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33

Zhou, Bojian, Michiel C. J. Bliemer, Xuhong Li, and Di Huang. "A modified truncated Newton algorithm for the logit-based stochastic user equilibrium problem." Applied Mathematical Modelling 39, no. 18 (September 2015): 5415–35. http://dx.doi.org/10.1016/j.apm.2015.01.010.

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34

Altinoz, O. Tolga, and A. Egemen Yilmaz. "Multiobjective Hooke–Jeeves algorithm with a stochastic Newton–Raphson-like step-size method." Expert Systems with Applications 117 (March 2019): 166–75. http://dx.doi.org/10.1016/j.eswa.2018.09.033.

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35

Kulkarni, Ankur A., and Vivek S. Borkar. "Finite dimensional approximation and Newton-based algorithm for stochastic approximation in Hilbert space." Automatica 45, no. 12 (December 2009): 2815–22. http://dx.doi.org/10.1016/j.automatica.2009.09.031.

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36

Wang, Xiaozhou, and Xiaojun Chen. "Solving Two-Stage Stochastic Variational Inequalities by a Hybrid Projection Semismooth Newton Algorithm." SIAM Journal on Scientific Computing 45, no. 4 (July 19, 2023): A1741—A1765. http://dx.doi.org/10.1137/22m1475302.

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37

Li, Changguo, Yongzhen Pei, Meixia Zhu, and Yue Deng. "Parameter Estimation on a Stochastic SIR Model with Media Coverage." Discrete Dynamics in Nature and Society 2018 (June 12, 2018): 1–7. http://dx.doi.org/10.1155/2018/3187807.

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Media coverage reduces the transmission rate from infective to susceptible individuals and is reflected by suitable nonlinear functions in mathematical modeling of the disease. We here focus on estimating the parameters in the transmission rate based on a stochastic SIR epidemic model with media coverage. In order to reduce the computational load, the Newton-Raphson algorithm and Markov Chain Monte Carlo (MCMC) technique are incorporated with maximum likelihood estimation. Simulations validate our estimation results and the necessity of a model with media coverage when modeling the contagious diseases.

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38

Chen, Minghan, Brandon D. Amos, Layne T. Watson, John J. Tyson, Young Cao, Clifford A. Shaffer, Michael W. Trosset, Cihan Oguz, and Gisella Kakoti. "Quasi-Newton Stochastic Optimization Algorithm for Parameter Estimation of a Stochastic Model of the Budding Yeast Cell Cycle." IEEE/ACM Transactions on Computational Biology and Bioinformatics 16, no. 1 (January 1, 2019): 301–11. http://dx.doi.org/10.1109/tcbb.2017.2773083.

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39

Montes, Francisco, and Jorge Mateu. "On the MLE for a spatial point pattern." Advances in Applied Probability 28, no. 2 (June 1996): 339. http://dx.doi.org/10.1017/s0001867800048382.

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Parameter estimation for a two-dimensional point pattern is difficult because most of the available stochastic models have intractable likelihoods ([2]). An exception is the class of Gibbs or Markov point processes ([1], [5]), where the likelihood typically forms an exponential family and is given explicitly up to a normalising constant. However, the latter is not known analytically, so parameter estimates must be based on approximations ([3], [6], [7]). In this paper we present comparisons amongst the different techniques available in the literature to obtain an approximation of the maximum likelihood estimate (MLE). Two stochastic methods are specifically illustrated: a Newton-Raphson algorithm ([7]) and the Robbins-Monro procedure ([8]). We use a very simple point process model, the Strauss process ([4]), to test and compare those approximations.

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40

Abdulkadirov, R. I., and P. A. Lyakhov. "A new approach to training neural networks using natural gradient descent with momentum based on Dirichlet distributions." Computer Optics 47, no. 1 (February 2023): 160–69. http://dx.doi.org/10.18287/2412-6179-co-1147.

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In this paper, we propose a natural gradient descent algorithm with momentum based on Dirichlet distributions to speed up the training of neural networks. This approach takes into account not only the direction of the gradients, but also the convexity of the minimized function, which significantly accelerates the process of searching for the extremes. Calculations of natural gradients based on Dirichlet distributions are presented, with the proposed approach introduced into an error backpropagation scheme. The results of image recognition and time series forecasting during the experiments show that the proposed approach gives higher accuracy and does not require a large number of iterations to minimize loss functions compared to the methods of stochastic gradient descent, adaptive moment estimation and adaptive parameter-wise diagonal quasi-Newton method for nonconvex stochastic optimization.

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41

Ding, Liang, and Jun Cao. "Electromagnetic Nondestructive Testing by Perturbation Homotopy Method." Mathematical Problems in Engineering 2014 (2014): 1–10. http://dx.doi.org/10.1155/2014/895159.

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Now electromagnetic nondestructive testing methods have been applied to many fields of engineering. But traditional electromagnetic methods (usually based on least square and local iteration) just roughly give the information of location, scale, and quality. In this paper we consider inverse electromagnetic problem which is concerned with the estimation of electric conductivity of Maxwell's equations (2D and 3D). A perturbation homotopy method combined with damping Gauss-Newton methods is applied to the inverse electromagnetic problem. This method differs from traditional homotopy method. The structure of homotopy function is similar to Tikhonov functional. Sets of solutions are produced by perturbation for every homotopy parameterλ=λi,i=0,…,L. At each iterative step of the algorithm, we add stochastic perturbation to numerical solutions. The previous solution and perturbation solution are regarded as the initial value in the next iteration. Although the number of solution in set increased, it increased the likelihood of obtaining correct solution. Results exhibits clear advantages over damping Gauss-Newton method and testify that it is an available method, especially on aspects of wide convergence and precision.

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42

Reyes, Jimmy, Inmaculada Barranco-Chamorro, Diego Gallardo, and Héctor Gómez. "Generalized Modified Slash Birnbaum–Saunders Distribution." Symmetry 10, no. 12 (December 6, 2018): 724. http://dx.doi.org/10.3390/sym10120724.

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In this paper, a generalization of the modified slash Birnbaum–Saunders (BS) distribution is introduced. The model is defined by using the stochastic representation of the BS distribution, where the standard normal distribution is replaced by a symmetric distribution proposed by Reyes et al. It is proved that this new distribution is able to model more kurtosis than other extensions of BS previously proposed in the literature. Closed expressions are given for the pdf (probability density functio), along with their moments, skewness and kurtosis coefficients. Inference carried out is based on modified moments method and maximum likelihood (ML). To obtain ML estimates, two approaches are considered: Newton–Raphson and EM-algorithm. Applications reveal that it has potential for doing well in real problems.

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43

Hung, Ching Pui, Allan Sacha Brun, Alexandre Fournier, Laurène Jouve, Olivier Talagrand, and Mustapha Zakari. "Towards Estimating the Solar Meridional Flow and Predicting the 11-yr Cycle Using Advanced Variational Data Assimilation Techniques." Proceedings of the International Astronomical Union 13, S335 (July 2017): 183–86. http://dx.doi.org/10.1017/s1743921317010754.

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AbstractWe present in this work the development of a solar data assimilation method based on an axisymmetric mean field dynamo model and magnetic surface data. Our mid-term goal is to predict the solar quasi cyclic activity. We focus on the ability of our variational data assimilation algorithm to constrain the deep meridional circulation of the Sun based on solar magnetic observations. Within a given assimilation window, the assimilation procedure minimizes the differences between data and the forecast from the model, by finding an optimal meridional circulation in the convection zone, and an optimal initial magnetic field, via a quasi-Newton algorithm. We demonstrate the capability of the technique to estimate the meridional flow by a closed-loop experiment involving 40 years of synthetic, solar-like data. We show that the method is robust in estimating a (stochastic) time-varying flow fluctuating 30% about the average, and that the horizon of predictability of the method is ~ 1 cycle length.

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44

Behboodi-Kahoo, Malihe, and Saeed Ketabchi. "Parallel implementation of augmented Lagrangian method within L-shaped method for stochastic linear programs." Filomat 31, no. 3 (2017): 799–808. http://dx.doi.org/10.2298/fil1703799b.

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In this paper, we study two-stage stochastic linear programming (SLP) problems with fixed recourse. The problem is often large scale as the objective function involves an expectation over a discrete set of scenarios. This paper presents a parallel implementation of the augmented Lagrangian method for solving SLPs. Our parallel method is based on a modified version of the L-shaped method and reducing linear master and recourse programs to unconstrained maximization of concave differentiable piecewise quadratic functions. The maximization problem is solved using the generalized Newton method. The parallel method is implemented in MATLAB. Large scale SLP with several millions of variables and several hundreds of thousands of constraints are solved. The results of uniprocessor and multiprocessor computations are presented which show that the parallel algorithm is effective.

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45

Cao, Pengfei, and Xionglin Luo. "Performance Analysis of The Auxiliary-Model-Based Multi-Innovation Stochastic Newton Recursive Algorithm for Dual-Rate Systems." Asian Journal of Control 19, no. 2 (October 18, 2016): 647–58. http://dx.doi.org/10.1002/asjc.1395.

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46

Seerwan Sulieman Noon. "Estimation the Variogram Function Indicator which represent the Transmissivity Coefficient in the groundwater." Tikrit Journal of Pure Science 25, no. 5 (December 18, 2020): 110–18. http://dx.doi.org/10.25130/tjps.v25i5.299.

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The problem tackled in this paper is the estimation of variogram function Indicator of spatial stochastic process for the Levels of groundwater, by the method of weighted Least squares. This methods is well known in regression analysis in estimating the coefficient of ression model. After defining the indicator variable the parameters of Indicator variogram estimated based on mean squares error. The final formula of weighted least squares estimator can be not be solved exactly, then through the use of iterative Newten - Raphson algorithm and for some iterations the convergence of solution is obtained with certain termination criterion or number of repeats (that used in this paper).

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47

León, Roberto, Pablo A. Miranda-Gonzalez, Francisco J. Tapia-Ubeda, and Elias Olivares-Benitez. "An Inventory Service-Level Optimization Problem for a Multi-Warehouse Supply Chain Network with Stochastic Demands." Mathematics 12, no. 16 (August 17, 2024): 2544. http://dx.doi.org/10.3390/math12162544.

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This research aims to develop a mathematical model and a solution approach for jointly optimizing a global inventory service level and order sizes for a single-commodity supply chain network with multiple warehouses or distribution centers. The latter face stochastic demands, such as most real-world supply chains do nowadays, yielding significant model complexity. The studied problem is of high relevance for inventory management, inventory location, and supply chain network design-related literature, as well as for logistics and supply chain managers. The proposed optimization model minimizes the total costs associated with cycle inventory, safety stock, and stock-out-related events, considering a global inventory service level and differentiated order sizes for a fixed and known set of warehouses. Subsequently, the model is solved by employing the Newton–Raphson algorithm, which is developed and implemented assuming stochastic demands with a normal approximation. The algorithm reached optimality conditions and the convergence criterion in a few iterations, within less than a second, for a variety of real-world sized instances involving up to 200 warehouses. The model solutions are contrasted with those obtained with a previous widely employed approximation, where safety stock costs were further approximated and order sizes were optimized without considering stock-out-related costs. This comparison denotes valuable benefits without significant additional computational efforts. Thus, the proposed approach is suitable for managers of real-world supply chains, since they would be able to attain system performance improvements by simultaneously optimizing the global inventory service level and order sizes, thereby providing a better system cost equilibrium.

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48

Zhou, Wei, and Jun Fang. "Probabilistic Analysis of Gun Barrel Ablation Life Based on the Modified Response Surface Model." Advanced Materials Research 1004-1005 (August 2014): 1076–83. http://dx.doi.org/10.4028/www.scientific.net/amr.1004-1005.1076.

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The randomness of structural and material parameters needs to be considered in the reliability analysis of gun barrel ablation life. However, the traditional method, like Stochastic FEM sampling, results in huge computing workload and low efficiency. This paper proposed a modified response surface model for estimating the gun barrel ablation life. In which, the estimation error of the response surface model is the optimization goal. Gauss-Newton method (GNM) is used to get the optimal solution whose initial value is solved by Genetic-algorithm (GA). After that, ablation life can be calculated by the optimized response surface model. GA is effective in global solution space searching, while GNM is effective in local searching. The new method takes full advantages of both GA and GNM in parameters estimation. The simulation result shows that the combination of GA and GNM obtains a higher precision of ablation estimation and greatly improves the computational efficiency.

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49

Regulski, Piotr A., Jakub Zielinski, Bartosz Borucki, and Krzysztof Nowinski. "A Weighted Stochastic Conjugate Direction Algorithm for Quantitative Magnetic Resonance Images—A Pattern in Ruptured Achilles Tendon T2-Mapping Assessment." Healthcare 10, no. 5 (April 23, 2022): 784. http://dx.doi.org/10.3390/healthcare10050784.

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This study presents an accurate biexponential weighted stochastic conjugate direction (WSCD) method for the quantitative T2-mapping reconstruction of magnetic resonance images (MRIs), and this approach was compared with the non-negative-least-squares Gauss–Newton (GN) numerical optimization method in terms of accuracy and goodness of fit of the reconstructed images from simulated data and ruptured Achilles tendon (AT) MRIs. Reconstructions with WSCD and GN were obtained from data simulating the signal intensity from biexponential decay and from 58 MR studies of postrupture, surgically repaired ATs. Both methods were assessed in terms of accuracy (closeness of the means of calculated and true simulated T2 values) and goodness of fit (magnitude of mean squared error (MSE)). The lack of significant deviation in correct T2 values for the WSCD method was demonstrated for SNR ≥ 20 and for GN–SNR ≥ 380. The MSEs for WSCD and GN were 287.52 ± 224.11 and 2553.91 ± 1932.31, respectively. The WSCD reconstruction method was better than the GN method in terms of accuracy and goodness of fit.

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50

Nikouei, Seyed Yahya, Behzad Mirzaeian Dehkordi, and Mehdi Niroomand. "A Genetic-Based Hybrid Algorithm Harmonic Minimization Method for Cascaded Multilevel Inverters with ANFIS Implementation." Mathematical Problems in Engineering 2021 (April 21, 2021): 1–15. http://dx.doi.org/10.1155/2021/6642317.

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Selective harmonic elimination pulse-width modulation (SHEPWM) is a widely adopted method to eliminate harmonics in multilevel inverters, yet solving harmonic amplitude equations is both time consuming and not accurate. This method is applied here for a 7-level cascaded multilevel inverter (CMLI) with erroneous DC sources. To meet the seven harmonic amplitude equations, two notches are applied with the use of higher switching frequency than nominal. These notches can be placed in six different positions in the voltage wave, and each was assessed in a separate manner. In order to solve the equations, a hybrid algorithm composed of genetic algorithm (GA) and Newton–Raphson (N-R) algorithm is applied to achieve faster convergence and maintain the accuracy of stochastic methods. At each step of the modulation index (M), different positions for the notches are compared based on the distortion factor (DF2%) benchmark, and the position with lowest DF2% is selected to train an artificial neural fuzzy interface system (ANFIS). ANFIS will receive the DC sources’ voltages together with required M and will produce one output; thus, eight ANFISs are applied to produce seven firing angles, and the remaining one is to determine which one of the notches’ positions should be used. Software simulations and experimental results confirm the validity of this proposed method. The proposed method achieves THD 8.45% when M is equal to 0.8 and is capable of effectively eliminating all harmonics up to the 19th order.

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