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Journal articles on the topic 'Active Set Newton Algorithm'

Author: Grafiati

Published: 6 September 2023

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1

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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2

Liang, Xi-ming. "Active set truncated-newton algorithm for simultaneous optimization of distillation column." Journal of Central South University of Technology 12, no. 1 (February 1, 2005): 93–96. http://dx.doi.org/10.1007/s11771-005-0211-x.

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3

San Juan Sebastián, Pablo, Tuomas Virtanen, Victor M. Garcia-Molla, and Antonio M. Vidal. "Analysis of an efficient parallel implementation of active-set Newton algorithm." Journal of Supercomputing 75, no. 3 (May 19, 2018): 1298–309. http://dx.doi.org/10.1007/s11227-018-2423-5.

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4

Virtanen, Tuomas, Jort Florent Gemmeke, and Bhiksha Raj. "Active-Set Newton Algorithm for Overcomplete Non-Negative Representations of Audio." IEEE Transactions on Audio, Speech, and Language Processing 21, no. 11 (November 2013): 2277–89. http://dx.doi.org/10.1109/tasl.2013.2263144.

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5

Sun, Li, Guoping He, Yongli Wang, and Changyin Zhou. "An accurate active set newton algorithm for large scale bound constrained optimization." Applications of Mathematics 56, no. 3 (May 20, 2011): 297–314. http://dx.doi.org/10.1007/s10492-011-0018-z.

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6

El-Alem, Mahmoud M., Mohammedi R. Abdel-Aziz, and Amr S. El-Bakry. "A projected Hessian Gauss-Newton algorithm for solving systems of nonlinear equations and inequalities." International Journal of Mathematics and Mathematical Sciences 25, no. 6 (2001): 397–409. http://dx.doi.org/10.1155/s0161171201002290.

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Solving systems of nonlinear equations and inequalities is of critical importance in many engineering problems. In general, the existence of inequalities in the problem adds to its difficulty. We propose a new projected Hessian Gauss-Newton algorithm for solving general nonlinear systems of equalities and inequalities. The algorithm uses the projected Gauss-Newton Hessian in conjunction with an active set strategy that identifies active inequalities and a trust-region globalization strategy that ensures convergence from any starting point. We also present a global convergence theory for the proposed algorithm.

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7

Facchinei, Francisco, Joaquim Júdice, and João Soares. "An Active Set Newton Algorithm for Large-Scale Nonlinear Programs with Box Constraints." SIAM Journal on Optimization 8, no. 1 (February 1998): 158–86. http://dx.doi.org/10.1137/s1052623493253991.

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8

Jodlbauer, Daniel, Ulrich Langer, and Thomas Wick. "Parallel Matrix-Free Higher-Order Finite Element Solvers for Phase-Field Fracture Problems." Mathematical and Computational Applications 25, no. 3 (July 7, 2020): 40. http://dx.doi.org/10.3390/mca25030040.

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Phase-field fracture models lead to variational problems that can be written as a coupled variational equality and inequality system. Numerically, such problems can be treated with Galerkin finite elements and primal-dual active set methods. Specifically, low-order and high-order finite elements may be employed, where, for the latter, only few studies exist to date. The most time-consuming part in the discrete version of the primal-dual active set (semi-smooth Newton) algorithm consists in the solutions of changing linear systems arising at each semi-smooth Newton step. We propose a new parallel matrix-free monolithic multigrid preconditioner for these systems. We provide two numerical tests, and discuss the performance of the parallel solver proposed in the paper. Furthermore, we compare our new preconditioner with a block-AMG preconditioner available in the literature.

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9

Lai, Shu-Zhen, Hou-Biao Li, and Zu-Tao Zhang. "A Symmetric Rank-One Quasi-Newton Method for Nonnegative Matrix Factorization." ISRN Applied Mathematics 2014 (January 22, 2014): 1–11. http://dx.doi.org/10.1155/2014/846483.

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As is well known, the nonnegative matrix factorization (NMF) is a dimension reduction method that has been widely used in image processing, text compressing, signal processing, and so forth. In this paper, an algorithm on nonnegative matrix approximation is proposed. This method is mainly based on a relaxed active set and the quasi-Newton type algorithm, by using the symmetric rank-one and negative curvature direction technologies to approximate the Hessian matrix. The method improves some recent results. In addition, some numerical experiments are presented in the synthetic data, imaging processing, and text clustering. By comparing with the other six nonnegative matrix approximation methods, this method is more robust in almost all cases.

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Falocco, S., F. J. Carrera, and J. Larsson. "Automated algorithms to build active galactic nucleus classifiers." Monthly Notices of the Royal Astronomical Society 510, no. 1 (November 27, 2021): 161–76. http://dx.doi.org/10.1093/mnras/stab3435.

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ABSTRACT We present a machine learning model to classify active galactic nuclei (AGNs) and galaxies (AGN-galaxy classifier) and a model to identify type 1 (optically unabsorbed) and type 2 (optically absorbed) AGN (type 1/2 classifier). We test tree-based algorithms, using training samples built from the X-ray Multi-Mirror Mission–Newton (XMM–Newton) catalogue and the Sloan Digital Sky Survey (SDSS), with labels derived from the SDSS survey. The performance was tested making use of simulations and of cross-validation techniques. With a set of features including spectroscopic redshifts and X-ray parameters connected to source properties (e.g. fluxes and extension), as well as features related to X-ray instrumental conditions, the precision and recall for AGN identification are 94 and 93 per cent, while the type 1/2 classifier has a precision of 74 per cent and a recall of 80 per cent for type 2 AGNs. The performance obtained with photometric redshifts is very similar to that achieved with spectroscopic redshifts in both test cases, while there is a decrease in performance when excluding redshifts. Our machine learning model trained on X-ray features can accurately identify AGN in extragalactic surveys. The type 1/2 classifier has a valuable performance for type 2 AGNs, but its ability to generalize without redshifts is hampered by the limited census of absorbed AGN at high redshift.

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11

Zhang, Shao Bo, Mei Li, and Yan Xia Liu. "Analysis and Optimization of Ride Comfort for Semi-Active Suspension Based on Variable Damping." Advanced Materials Research 1055 (November 2014): 175–81. http://dx.doi.org/10.4028/www.scientific.net/amr.1055.175.

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Based on NEWTON and dynamical analysis the half car model is built, in which air spring is a nonlinear system on the basis of force model and the shock absorber has soft and hard states. By the simulation of the model and combination with experiments, the model is proved right and the influencing factor of angle-displacement and acceleration of body can be gained. Then with the application of genetic algorithm in Matlab tools, appropriate control parameters is being set, the above-mentioned model can be optimized, results of optimizations will be compared with three ride comfort evaluation indexes before optimizations. By judging the corresponded extents of curve before and after optimizations, it shows that the parameters after optimizations can improve the ride comfort.

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12

Lan, Lei, Minchen Li, Chenfanfu Jiang, Huamin Wang, and Yin Yang. "Second-order Stencil Descent for Interior-point Hyperelasticity." ACM Transactions on Graphics 42, no. 4 (July 26, 2023): 1–16. http://dx.doi.org/10.1145/3592104.

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In this paper, we present a GPU algorithm for finite element hyperelastic simulation. We show that the interior-point method, known to be effective for robust collision resolution, can be coupled with non-Newton procedures and be massively sped up on the GPU. Newton's method has been widely chosen for the interior-point family, which fully solves a linear system at each step. After that, the active set associated with collision/contact constraints is updated. Mimicking this routine using a non-Newton optimization (like gradient descent or ADMM) unfortunately does not deliver expected accelerations. This is because the barrier functions employed in an interior-point method need to be updated at every iteration to strictly confine the search to the feasible region. The associated cost (e.g., per-iteration CCD) quickly overweights the benefit brought by the GPU, and a new parallelism modality is needed. Our algorithm is inspired by the domain decomposition method and designed to move interior-point-related computations to local domains as much as possible. We minimize the size of each domain (i.e., a stencil) by restricting it to a single element, so as to fully exploit the capacity of modern GPUs. The stencil-level results are integrated into a global update using a novel hybrid sweep scheme. Our algorithm is locally second-order offering better convergence. It enables simulation acceleration of up to two orders over its CPU counterpart. We demonstrate the scalability, robustness, efficiency, and quality of our algorithm in a variety of simulation scenarios with complex and detailed collision geometries.

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13

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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14

Haslinger, Jaroslav, Radek Kučera, Kristina Motyčková, and Václav Šátek. "Numerical Modeling of the Leak through Semipermeable Walls for 2D/3D Stokes Flow: Experimental Scalability of Dual Algorithms." Mathematics 9, no. 22 (November 15, 2021): 2906. http://dx.doi.org/10.3390/math9222906.

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The paper deals with the Stokes flow subject to the threshold leak boundary conditions in two and three space dimensions. The velocity–pressure formulation leads to the inequality type problem that is approximated by the P1-bubble/P1 mixed finite elements. The resulting algebraic system is nonsmooth. It is solved by the path-following variant of the interior point method, and by the active-set implementation of the semi-smooth Newton method. Inner linear systems are solved by the preconditioned conjugate gradient method. Numerical experiments illustrate scalability of the algorithms. The novelty of this work consists in applying dual strategies for solving the problem.

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15

Stefanova, Maria, Olga Minevich, Stanislav Baklanov, Margarita Petukhova, Sergey Lupuleac, Boris Grigor’ev, and Michael Kokkolaras. "Convex optimization techniques in compliant assembly simulation." Optimization and Engineering 21, no. 4 (March 6, 2020): 1665–90. http://dx.doi.org/10.1007/s11081-020-09493-z.

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Abstract A special class of quadratic programming (QP) problems is considered in this paper. This class emerges in simulation of assembly of large-scale compliant parts, which involves the formulation and solution of contact problems. The considered QP problems can have up to 20,000 unknowns, the Hessian matrix is fully populated and ill-conditioned, while the matrix of constraints is sparse. Variation analysis and optimization of assembly process usually require massive computations of QP problems with slightly different input data. The following optimization methods are adapted to account for the particular features of the assembly problem: an interior point method, an active-set method, a Newton projection method, and a pivotal algorithm for the linear complementarity problems. Equivalent formulations of the QP problem are proposed with the intent of them being more amenable to the considered methods. The methods are tested and results are compared for a number of aircraft assembly simulation problems.

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16

Pennock, Clara M., Jacco Th van Loon, Cameron P. M. Bell, Miroslav D. Filipović, Tana D. Joseph, and Eleni Vardoulaki. "Discovering exotic AGN behind the Magellanic Clouds." Proceedings of the International Astronomical Union 15, S356 (October 2019): 335–38. http://dx.doi.org/10.1017/s1743921320003270.

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AbstractThe nearby Magellanic Clouds system covers more than 200 square degrees on the sky. Much of it has been mapped across the electromagnetic spectrum at high angular resolution and sensitivity â€“X-ray (XMM-Newton), UV (UVIT), optical (SMASH), IR (VISTA, WISE, Spitzer, Herschel), radio (ATCA, ASKAP, MeerKAT). This provides us with an excellent dataset to explore the galaxy populations behind the stellar-rich Magellanic Clouds. We seek to identify and characterise AGN via machine learning algorithms on this exquisite data set. Our project focuses not on establishing sequences and distributions of common types of galaxies and active galactic nuclei (AGN), but seeks to identify extreme examples, building on the recent accidental discoveries of unique AGN behind the Magellanic Clouds.

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17

Wohlmuth, Barbara. "Variationally consistent discretization schemes and numerical algorithms for contact problems." Acta Numerica 20 (April 28, 2011): 569–734. http://dx.doi.org/10.1017/s0962492911000079.

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We consider variationally consistent discretization schemes for mechanical contact problems. Most of the results can also be applied to other variational inequalities, such as those for phase transition problems in porous media, for plasticity or for option pricing applications from finance. The starting point is to weakly incorporate the constraint into the setting and to reformulate the inequality in the displacement in terms of a saddle-point problem. Here, the Lagrange multiplier represents the surface forces, and the constraints are restricted to the boundary of the simulation domain. Having a uniform inf-sup bound, one can then establish optimal low-ordera prioriconvergence rates for the discretization error in the primal and dual variables. In addition to the abstract framework of linear saddle-point theory, complementarity terms have to be taken into account. The resulting inequality system is solved by rewriting it equivalently by means of the non-linear complementarity function as a system of equations. Although it is not differentiable in the classical sense, semi-smooth Newton methods, yielding super-linear convergence rates, can be applied and easily implemented in terms of a primal–dual active set strategy. Quite often the solution of contact problems has a low regularity, and the efficiency of the approach can be improved by using adaptive refinement techniques. Different standard types, such as residual- and equilibrated-baseda posteriorierror estimators, can be designed based on the interpretation of the dual variable as Neumann boundary condition. For the fully dynamic setting it is of interest to apply energy-preserving time-integration schemes. However, the differential algebraic character of the system can result in high oscillations if standard methods are applied. A possible remedy is to modify the fully discretized system by a local redistribution of the mass. Numerical results in two and three dimensions illustrate the wide range of possible applications and show the performance of the space discretization scheme, non-linear solver, adaptive refinement process and time integration.

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18

Cheng, Wanyou, and Yu-Hong Dai. "An active set Newton-CG method for ℓ1 optimization." Applied and Computational Harmonic Analysis 50 (January 2021): 303–25. http://dx.doi.org/10.1016/j.acha.2019.08.005.

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19

Daryina, A. N., A. F. Izmailov, and M. V. Solodov. "A Class of Active-Set Newton Methods for Mixed ComplementarityProblems." SIAM Journal on Optimization 15, no. 2 (January 2005): 409–29. http://dx.doi.org/10.1137/s105262340343590x.

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20

Izmailov, A. F., and A. L. Pogosyan. "Active-set Newton methods for mathematical programs with vanishing constraints." Computational Optimization and Applications 53, no. 2 (March 7, 2012): 425–52. http://dx.doi.org/10.1007/s10589-012-9467-x.

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21

Drissi-Kaïtouni, Omar, and Michael Florian. "An active constraints Newton algorithm for the spatial price equilibrium problem." European Journal of Operational Research 72, no. 1 (January 1994): 155–66. http://dx.doi.org/10.1016/0377-2217(94)90337-9.

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22

Pho, Kim-Hung, and Vu-Thanh Nguyen. "Comparison of Newton-Raphson Algorithm and Maxlik Function." Journal of Advanced Engineering and Computation 2, no. 4 (December 31, 2018): 281. http://dx.doi.org/10.25073/jaec.201824.219.

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Our main objective is in antagonizing the performance of two approaches: the Newton-Raphson (N-R) algorithm and maxLik function in the statistical software R to obtain optimization roots of estimating functions. We present the approach of algorithms, examples and discussing about two approaches in detail. Besides, we prove that the N-R algorithm can perform if our data set contain missing values, while maxLik function cannot execute in this situation. In addition, we also compare the results, as well as, the time to run code to output the result of two approaches through an example is introduced in [1].This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.

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23

Izmailov, A. F., and M. V. Solodov. "An Active-Set Newton Method for Mathematical Programs with Complementarity Constraints." SIAM Journal on Optimization 19, no. 3 (January 2008): 1003–27. http://dx.doi.org/10.1137/070690882.

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24

Hintermüller, M., K. Ito, and K. Kunisch. "The Primal-Dual Active Set Strategy as a Semismooth Newton Method." SIAM Journal on Optimization 13, no. 3 (January 2002): 865–88. http://dx.doi.org/10.1137/s1052623401383558.

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25

Essanhaji, A., and M. Errachid. "Lagrange Multivariate Polynomial Interpolation: A Random Algorithmic Approach." Journal of Applied Mathematics 2022 (March 14, 2022): 1–8. http://dx.doi.org/10.1155/2022/8227086.

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The problems of polynomial interpolation with several variables present more difficulties than those of one-dimensional interpolation. The first problem is to study the regularity of the interpolation schemes. In fact, it is well-known that, in contrast to the univariate case, there is no universal space of polynomials which admits unique Lagrange interpolation for all point sets of a given cardinality, and so the interpolation space will depend on the set Z of interpolation points. Techniques of univariate Newton interpolating polynomials are extended to multivariate data points by different generalizations and practical algorithms. The Newton basis format, with divided-difference algorithm for coefficients, generalizes in a straightforward way when interpolating at nodes on a grid within certain schemes. In this work, we propose a random algorithm for computing several interpolating multivariate Lagrange polynomials, called RLMVPIA (Random Lagrange Multivariate Polynomial Interpolation Algorithm), for any finite interpolation set. We will use a Newton-type polynomials basis, and we will introduce a new concept called Z , z -partition. All the given algorithms are tested on examples. RLMVPIA is easy to implement and requires no storage.

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26

Farikha, Ema Fahma, Rusli Hidayat, and Muhammad Ziaul Arif. "PENERAPAN COCKROACH SWARM OPTIMIZATION ALGORITHM (CSOA) PADA PENYELESAIAN PERSAMAAN POLINOMIAL YANG MEMILIKI AKAR KOMPLEKS." Majalah Ilmiah Matematika dan Statistika 18, no. 2 (September 3, 2018): 81. http://dx.doi.org/10.19184/mims.v18i2.17251.

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In this paper, we use a metaheuristic algorithm for solving non-linear equations (polynomial equations) which have a set of complex roots (complex numbers). The metaheuristic algorithm is the Cockroach Swarm Optimization Algorithm (CSOA) which imitate various types of natural cockroach behaviors such as chase-swarming, dispersing and ruthlessness when hunting for food sources. In this study, several examples of non-linear polynomial equations were used for evaluating the accuracy of CSOA. In this simulation, the accuracy comparison has been accomplished. It is shown that CSOA results are more accurate compared to the Newton-Raphson results. Keywords: Cockroach Swarm Optimization Algorithm, Complex roots of polynomial, Newton-Raphson, Non-Linear equation.

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27

Aree, Pichai. "Newton-Raphson Power-Flow Analysis Including Induction Motor Loads." ECTI Transactions on Electrical Engineering, Electronics, and Communications 10, no. 1 (July 31, 2011): 74–79. http://dx.doi.org/10.37936/ecti-eec.2012101.170466.

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This paper presents an extended method of Newton-Raphson power flow algorithm to incorporate nonlinear model of induction motor loads. The proposed method is used for finding correct power system operating conditions, which can be employed for solving the problem of initializing the dynamic models of induction motor for stability studies. The power flow solution with a group of induction motor loads is demonstrated through 14buses industrial power system. Moreover, the computational efficiency of the extended algorithm has been investigated using IEEE-30buses network. The results show that this algorithm gives an exact solution of motor’s active and reactive powers that are related with converged slips, terminal voltages, and mechanical torque profiles. Furthermore, the extended algorithm shows a good convergent characteristic in quadratic manner.

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28

Kružík, J., D. Horák, M. Čermák, L. Pospíšil, and M. Pecha. "Active set expansion strategies in MPRGP algorithm." Advances in Engineering Software 149 (November 2020): 102895. http://dx.doi.org/10.1016/j.advengsoft.2020.102895.

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29

Zhang, Li Pu, and Ying Hong Xu. "An Efficient Algorithm for Linear Complementarity Problems." Advanced Materials Research 204-210 (February 2011): 687–90. http://dx.doi.org/10.4028/www.scientific.net/amr.204-210.687.

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Through some modifications on the classical-Newton direction, we obtain a new searching direction for monotone horizontal linear complementarity problem. By taking the step size along this direction as one, we set up a full-step primal-dual interior-point algorithm for monotone horizontal linear complementarity problem. The complexity bound for the algorithm is derived, which is the best-known for linear complementarity problem.

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30

Porcelli, Margherita, Valeria Simoncini, and Mattia Tani. "Preconditioning of Active-Set Newton Methods for PDE-constrained Optimal Control Problems." SIAM Journal on Scientific Computing 37, no. 5 (January 2015): S472—S502. http://dx.doi.org/10.1137/140975711.

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31

Cheng, Wanyou, Zixin Chen, and Dong-hui Li. "An active set truncated Newton method for large-scale bound constrained optimization." Computers & Mathematics with Applications 67, no. 5 (March 2014): 1016–23. http://dx.doi.org/10.1016/j.camwa.2014.01.009.

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32

Luo, Yiping, Jinhao Meng, Defa Wang, and Guobin Xue. "New One-Dimensional Search Iteration Algorithm and Engineering Application." Shock and Vibration 2021 (November 2, 2021): 1–11. http://dx.doi.org/10.1155/2021/7643555.

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In structural optimization design, obtaining the optimal solution of the objective function is the key to optimal design, and one-dimensional search is one of the important methods for function optimization. The Golden Section method is the main method of one-dimensional search, which has better convergence and stability. Based on the solution of the Golden Section method, this paper proposes an efficient one-dimensional search algorithm, which has the advantages of fast convergence and good stability. An objective function calculation formula is introduced to compare and analyse this method with the Golden Section method, Newton method, and Fibonacci method. It is concluded that when the accuracy is set to 0.1, the new algorithm needs 3 iterations to obtain the target value. The Golden Section method takes 11 iterations, and the Fibonacci method requires 11 iterations. The Newton method cannot obtain the target value. When the accuracy is set to 0.01, the number of iterations of the new method is still the least. The optimized design of the T-section beam is introduced for engineering application research. When the accuracy is set to 0.1, the new method needs 3 iterations to obtain the target value and the Golden Section method requires 13 iterations. When the accuracy is set to 0.01, the new method requires 4 iterations and the Golden Section method requires 18 iterations. The new method has significant advantages in the one-dimensional search optimization problem.

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33

YU, CHANGHUA, MICHAEL T. MANRY, and JIANG LI. "EFFECTS OF NONSINGULAR PREPROCESSING ON FEEDFORWARD NETWORK TRAINING." International Journal of Pattern Recognition and Artificial Intelligence 19, no. 02 (March 2005): 217–47. http://dx.doi.org/10.1142/s0218001405004022.

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In the neural network literature, many preprocessing techniques, such as feature de-correlation, input unbiasing and normalization, are suggested to accelerate multilayer perceptron training. In this paper, we show that a network trained with an original data set and one trained with a linear transformation of the original data will go through the same training dynamics, as long as they start from equivalent states. Thus preprocessing techniques may not be helpful and are merely equivalent to using a different weight set to initialize the network. Theoretical analyses of such preprocessing approaches are given for conjugate gradient, back propagation and the Newton method. In addition, an efficient Newton-like training algorithm is proposed for hidden layer training. Experiments on various data sets confirm the theoretical analyses and verify the improvement of the new algorithm.

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Triki, Chefi. "Solving the Flood Propagation Problem with Newton Algorithm on Parallel Systems." Sultan Qaboos University Journal for Science [SQUJS] 16 (April 1, 2012): 147. http://dx.doi.org/10.24200/squjs.vol17iss1pp147-156.

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In this paper we propose a parallel implementation for the flood propagation method Flo2DH. The model is built on a finite element spatial approximation combined with a Newton algorithm that uses a direct LU linear solver. The parallel implementation has been developed by using the standard MPI protocol and has been tested on a set of real world problems.

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35

Terzija, V., V. Stanojevic, Z. Lazarevic, and M. Popov. "Active and Reactive Power Metering in Non-Sinusoidal Conditions Using Newton Type Algorithm." Renewable Energy and Power Quality Journal 1, no. 03 (March 2005): 241–45. http://dx.doi.org/10.24084/repqj03.265.

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36

Zhu, Liping, Xiaojun Qiu, Dongxing Mao, Sheng Wu, and Xu Zhong. "Efficient segment-update block LMS-Newton algorithm for active control of road noise." Mechanical Systems and Signal Processing 198 (September 2023): 110436. http://dx.doi.org/10.1016/j.ymssp.2023.110436.

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37

Rakowska, J., R. T. Haftka, and L. T. Watson. "An active set algorithm for tracing parametrized optima." Structural Optimization 3, no. 1 (March 1991): 29–44. http://dx.doi.org/10.1007/bf01743487.

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38

Hristov, D. H., and B. G. Fallone. "An active set algorithm for treatment planning optimization." Medical Physics 24, no. 9 (September 1997): 1455–64. http://dx.doi.org/10.1118/1.598034.

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39

Mustafa, Ahmed. "THE NEW RANK ONE CLASS FOR UNCONSTRAINED PROBLEMS SOLVING." Science Journal of University of Zakho 11, no. 2 (April 25, 2023): 185–89. http://dx.doi.org/10.25271/sjuoz.2023.11.2.1049.

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One of the most well-known methods for unconstrained problems is the quasi-Newton approach, iterative solutions. The great precision and quick convergence of the quasi-Newton methods are well recognized. In this work, the new algorithm for the symmetric rank one SR1 method is driven. The strong Wolfe line search criteria deﬁne the step length selection. We also proved the new quasi-Newton equation and positive definite matrix theorem. Preliminary computer testing on the set of fourteen unrestricted optimization test functions leads to the conclusion that this new method is more effective and durable than the implementation of classical SR1 method in terms of iterations count and functions.

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Yu, Zhensheng, and Peixin Li. "An active set quasi-Newton method with projection step for monotone nonlinear equations." AIMS Mathematics 6, no. 4 (2021): 3606–23. http://dx.doi.org/10.3934/math.2021215.

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Sun, Li, Guoping He, Yongli Wang, and Liang Fang. "An active set quasi-Newton method with projected search for bound constrained minimization." Computers & Mathematics with Applications 58, no. 1 (July 2009): 161–70. http://dx.doi.org/10.1016/j.camwa.2009.03.085.

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Rymarczyk, Tomasz, and Paweł Tchórzewski. "HYBRID TECHNIQUES TO SOLVE OPTIMIZATION PROBLEMS IN EIT." Informatics Control Measurement in Economy and Environment Protection 7, no. 1 (March 30, 2017): 72–75. http://dx.doi.org/10.5604/01.3001.0010.4587.

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This paper presents the hybrid algorithm for identification the unknown shape of an interface to solve the inverse problem in electrical impedance tomography. The conductivity values in different regions are determined by the finite element method. The numerical algorithm is a combination of the level set method, Gauss-Newton method and the finite element method. The representation of the shape of the boundary and its evolution during an iterative reconstruction process is achieved by the level set function. The cost of the numerical algorithm is enough effective. These algorithms are a relatively new procedure to overcome this problem.

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Borges-Quintana, M., M. A. Borges-Trenard, I. Márquez-Corbella, and E. Martínez-Moro. "Computing coset leaders and leader codewords of binary codes." Journal of Algebra and Its Applications 14, no. 08 (April 27, 2015): 1550128. http://dx.doi.org/10.1142/s0219498815501285.

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In this paper we use the Gröbner representation of a binary linear code [Formula: see text] to give efficient algorithms for computing the whole set of coset leaders, denoted by [Formula: see text] and the set of leader codewords, denoted by [Formula: see text]. The first algorithm could be adapted to provide not only the Newton and the covering radius of [Formula: see text] but also to determine the coset leader weight distribution. Moreover, providing the set of leader codewords we have a test-set for decoding by a gradient-like decoding algorithm. Another contribution of this article is the relation established between zero neighbors and leader codewords.

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Cheng, ZiLong, Jia Liu, MingFeng Zhang, Nan Zhao, MengYuan Wang, and YunXi Zhang. "Attitude Control Design and Simulation Analysis of Quadrotor Based on Active Disturbance Rejection Control." Journal of Physics: Conference Series 2216, no. 1 (March 1, 2022): 012031. http://dx.doi.org/10.1088/1742-6596/2216/1/012031.

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Abstract In this paper, the attitude control problem based on active disturbance rejection control (ADRC) is studied for nonlinear underactuated quadrotor aircraft with parametric uncertainties and modeling disturbances. The simplified dynamics model of the quadrotor is established by using Newton-Euler equation, and the ADRC is applied to control the attitude control of the quadrotor. Finally, through numerical simulations, the performance of the ADRC and traditional PID algorithm are compared, the results show that the attitude control algorithm based on ADRC has better performance, and has excellent ability to resist disturbance.

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SHUTTLEWORTH, I. G. "IMPROVEMENTS TO THE RADIUS OF CONVERGENCE OF DIRECT INVERSION TECHNIQUES IN HELIUM ATOM SCATTERING." Surface Review and Letters 15, no. 05 (October 2008): 519–23. http://dx.doi.org/10.1142/s0218625x08011718.

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Recent studies (I. G. Shuttleworth, Surf. Rev. Lett.14(2) (2007) 321) have demonstrated a direct method of diffraction pattern inversion for the helium atom scattering (HAS) experiment. The method requires the expansion of the Patterson function as a multivariate Taylor series to form a set of simultaneous equations. Benchmark tests of the procedure show that incomplete Taylor expansions introduce inconsistency into the set of simultaneous equations, whereas larger Taylor expansions attract significant numerical errors during their solution. The current work replaces the conventional matrix inversion techniques with a multidimensional Newton–Raphson algorithm. Tests have shown that the Newton–Raphson procedure removes the Taylor series and numerical limitations from the inversion technique for any realistic surface.

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Tomova, Anna. "Problems and solutions by the application of Julia set theory to one-dot and multi-dots numerical methods." International Journal of Mathematics and Mathematical Sciences 28, no. 9 (2001): 545–48. http://dx.doi.org/10.1155/s0161171201011887.

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In 1977 Hubbard developed the ideas of Cayley (1879) and solved in particular the Newton-Fourier imaginary problem. We solve the Newton-Fourier and the Chebyshev-Fourier imaginary problems completely. It is known that the application of Julia set theory is possible to the one-dot numerical method like the Newton's method for computing solution of the nonlinear equations. The secants method is the two-dots numerical method and the application of Julia set theory to it is not demonstrated. Previously we have defined two one-dot combinations: the Newton's-secants and the Chebyshev's-secants methods and have used the escape time algorithm to analyse the application of Julia set theory to these two combinations in some special cases. We consider and solve the Newton's-secants and Tchebicheff's-secants imaginary problems completely.

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Liu, Xiangjing, and Jianke Zhang. "Strong Convergence of a Two-Step Modified Newton Method for Weighted Complementarity Problems." Axioms 12, no. 8 (July 28, 2023): 742. http://dx.doi.org/10.3390/axioms12080742.

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This paper focuses on the weighted complementarity problem (WCP), which is widely used in the fields of economics, sciences and engineering. Not least because of its local superlinear convergence rate, smoothing Newton methods have widespread application in solving various optimization problems. A two-step smoothing Newton method with strong convergence is proposed. With a smoothing complementary function, the WCP is reformulated as a smoothing set of equations and solved by the proposed two-step smoothing Newton method. In each iteration, the new method computes the Newton equation twice, but using the same Jacobian, which can avoid consuming a lot of time in the calculation. To ensure the global convergence, a derivative-free line search rule is inserted. At the same time, we develop a different term in the solution of the smoothing Newton equation, which guarantees the local strong convergence. Under appropriate conditions, the algorithm has at least quadratic or even cubic local convergence. Numerical experiments indicate the stability and effectiveness of the new method. Moreover, compared to the general smoothing Newton method, the two-step smoothing Newton method can significantly improve the computational efficiency without increasing the computational cost.

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Hager, William W., and Hongchao Zhang. "A New Active Set Algorithm for Box Constrained Optimization." SIAM Journal on Optimization 17, no. 2 (January 2006): 526–57. http://dx.doi.org/10.1137/050635225.

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Nilsson, Björn, and Anders Heyden. "A fast algorithm for level set-like active contours." Pattern Recognition Letters 24, no. 9-10 (June 2003): 1331–37. http://dx.doi.org/10.1016/s0167-8655(02)00374-4.

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Milman, R., and E. J. Davison. "A Fast MPC Algorithm Using Nonfeasible Active Set Methods." Journal of Optimization Theory and Applications 139, no. 3 (May 7, 2008): 591–616. http://dx.doi.org/10.1007/s10957-008-9413-3.

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