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Journal articles on the topic 'Pathwise optimization'

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Author: Grafiati

Published: 10 December 2022

Last updated: 28 January 2023

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1

Friedman, Jerome, Trevor Hastie, Holger Höfling, and Robert Tibshirani. "Pathwise coordinate optimization." Annals of Applied Statistics 1, no. 2 (December 2007): 302–32. http://dx.doi.org/10.1214/07-aoas131.

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2

Desai, Vijay V., Vivek F. Farias, and Ciamac C. Moallemi. "Pathwise Optimization for Optimal Stopping Problems." Management Science 58, no. 12 (December 2012): 2292–308. http://dx.doi.org/10.1287/mnsc.1120.1551.

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3

Rogers, L. C. G. "Pathwise Stochastic Optimal Control." SIAM Journal on Control and Optimization 46, no. 3 (January 2007): 1116–32. http://dx.doi.org/10.1137/050642885.

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4

Pra, Paolo Dai, Giovanni B. Di Masi, and Barbara Trivellato. "Pathwise Optimality in Stochastic Control." SIAM Journal on Control and Optimization 39, no. 5 (January 2000): 1540–57. http://dx.doi.org/10.1137/s0363012998334778.

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5

Zhao, Tuo, Han Liu, and Tong Zhang. "Pathwise coordinate optimization for sparse learning: Algorithm and theory." Annals of Statistics 46, no. 1 (February 2018): 180–218. http://dx.doi.org/10.1214/17-aos1547.

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6

Davis, M. H. A., and M. P. Spathopoulos. "Pathwise Nonlinear Filtering for Nondegenerate Diffusions with Noise Correlation." SIAM Journal on Control and Optimization 25, no. 2 (March 1987): 260–78. http://dx.doi.org/10.1137/0325016.

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7

Jin, Xing, Dan Luo, and Xudong Zeng. "Dynamic Asset Allocation with Uncertain Jump Risks: A Pathwise Optimization Approach." Mathematics of Operations Research 43, no. 2 (May 2018): 347–76. http://dx.doi.org/10.1287/moor.2017.0854.

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8

Lin, Bingqing, Zhen Pang, and Jiming Jiang. "Fixed and Random Effects Selection by REML and Pathwise Coordinate Optimization." Journal of Computational and Graphical Statistics 22, no. 2 (April 2013): 341–55. http://dx.doi.org/10.1080/10618600.2012.681219.

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9

Prieto-Rumeau, Tomás, and Onésimo Hernández-Lerma. "Ergodic Control of Continuous-Time Markov Chains with Pathwise Constraints." SIAM Journal on Control and Optimization 47, no. 4 (January 2008): 1888–908. http://dx.doi.org/10.1137/060668857.

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10

Ai, Zidong. "Stabilization and optimization of linear systems via pathwise state-feedback impulsive control." Journal of the Franklin Institute 354, no. 3 (February 2017): 1637–57. http://dx.doi.org/10.1016/j.jfranklin.2016.12.005.

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11

Hinz, Juri, Tanya Tarnopolskaya, and Jeremy Yee. "Efficient algorithms of pathwise dynamic programming for decision optimization in mining operations." Annals of Operations Research 286, no. 1-2 (June 4, 2018): 583–615. http://dx.doi.org/10.1007/s10479-018-2910-3.

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12

Bonaccorsi, Stefano, Francesca Cottini, and Delio Mugnolo. "Random Evolution Equations: Well-Posedness, Asymptotics, and Applications to Graphs." Applied Mathematics & Optimization 84, no. 3 (March 11, 2021): 2849–87. http://dx.doi.org/10.1007/s00245-020-09732-w.

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AbstractWe study diffusion-type equations supported on structures that are randomly varying in time. After settling the issue of well-posedness, we focus on the asymptotic behavior of solutions: our main result gives sufficient conditions for pathwise convergence in norm of the (random) propagator towards a (deterministic) steady state. We apply our findings in two environments with randomly evolving features: ensembles of difference operators on combinatorial graphs, or else of differential operators on metric graphs.

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13

Mendoza-Pérez, Armando F., and Onésimo Hernández-Lerma. "Variance-minimization of Markov control processes with pathwise constraints." Optimization 61, no. 12 (December 2012): 1427–47. http://dx.doi.org/10.1080/02331934.2011.565762.

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14

Fontes, Fernando A. C. C., and Sofia O. Lopes. "Normal forms of necessary conditions for dynamic optimization problems with pathwise inequality constraints." Journal of Mathematical Analysis and Applications 399, no. 1 (March 2013): 27–37. http://dx.doi.org/10.1016/j.jmaa.2012.09.049.

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15

Caraballo, T., and P. E. Kloeden. "The Pathwise Numerical Approximation of Stationary Solutions of Semilinear Stochastic Evolution Equations." Applied Mathematics and Optimization 54, no. 3 (October 9, 2006): 401–15. http://dx.doi.org/10.1007/s00245-006-0876-z.

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16

Jack, Andrew, and Mihail Zervos. "Impulse Control of One-Dimensional Ito Diffusions with an Expected and a Pathwise Ergodic Criterion." Applied Mathematics and Optimization 54, no. 1 (April 28, 2006): 71–93. http://dx.doi.org/10.1007/s00245-005-0853-y.

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17

Mayne, David, and Richard Vinter. "First-Order Necessary Conditions in Optimal Control." Journal of Optimization Theory and Applications 189, no. 3 (March 26, 2021): 716–43. http://dx.doi.org/10.1007/s10957-021-01845-8.

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AbstractIn an earlier analysis of strong variation algorithms for optimal control problems with endpoint inequality constraints, Mayne and Polak provided conditions under which accumulation points satisfy a condition requiring a certain optimality function, used in the algorithms to generate search directions, to be nonnegative for all controls. The aim of this paper is to clarify the nature of this optimality condition, which we call the first-order minimax condition, and of a related integrated form of the condition, which, also, is implicit in past algorithm convergence analysis. We consider these conditions, separately, when a pathwise state constraint is, and is not, included in the problem formulation. When there are no pathwise state constraints, we show that the integrated first-order minimax condition is equivalent to the minimum principle and that the minimum principle (and equivalent integrated first-order minimax condition) is strictly stronger than the first-order minimax condition. For problems with state constraints, we establish that the integrated first-order minimax condition and the minimum principle are, once again, equivalent. But, in the state constrained context, it is no longer the case that the minimum principle is stronger than the first-order minimax condition, or vice versa. An example confirms the perhaps surprising fact that the first-order minimax condition is a distinct optimality condition that can provide information, for problems with state constraints, in some circumstances when the minimum principle fails to do so.

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18

Cardaliaguet, P., and C. Rainer. "Pathwise Strategies for Stochastic Differential Games with an Erratum to “Stochastic Differential Games with Asymmetric Information”." Applied Mathematics & Optimization 68, no. 1 (March 14, 2013): 75–84. http://dx.doi.org/10.1007/s00245-013-9198-0.

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19

Kushner, Harold J. "Approximations and Optimal Control for the Pathwise Average Cost Per Unit Time and Discounted Problems for Wideband Noise-Driven Systems." SIAM Journal on Control and Optimization 27, no. 3 (May 1989): 546–62. http://dx.doi.org/10.1137/0327029.

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20

Vaddireddy, Harsha, and Omer San. "Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach." Fluids 4, no. 2 (June 15, 2019): 111. http://dx.doi.org/10.3390/fluids4020111.

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Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach.

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21

Angiuli, Andrea, Christy V. Graves, Houzhi Li, Jean-François Chassagneux, François Delarue, and René Carmona. "Cemracs 2017: numerical probabilistic approach to MFG." ESAIM: Proceedings and Surveys 65 (2019): 84–113. http://dx.doi.org/10.1051/proc/201965084.

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This project investigates numerical methods for solving fully coupled forward-backward stochastic differential equations (FBSDEs) of McKean-Vlasov type. Having numerical solvers for such mean field FBSDEs is of interest because of the potential application of these equations to optimization problems over a large population, say for instance mean field games (MFG) and optimal mean field control problems. Theory for this kind of problems has met with great success since the early works on mean field games by Lasry and Lions, see [29], and by Huang, Caines, and Malhamé, see [26]. Generally speaking, the purpose is to understand the continuum limit of optimizers or of equilibria (say in Nash sense) as the number of underlying players tends to infinity. When approached from the probabilistic viewpoint, solutions to these control problems (or games) can be described by coupled mean field FBSDEs, meaning that the coefficients depend upon the own marginal laws of the solution. In this note, we detail two methods for solving such FBSDEs which we implement and apply to five benchmark problems. The first method uses a tree structure to represent the pathwise laws of the solution, whereas the second method uses a grid discretization to represent the time marginal laws of the solutions. Both are based on a Picard scheme; importantly, we combine each of them with a generic continuation method that permits to extend the time horizon (or equivalently the coupling strength between the two equations) for which the Picard iteration converges.

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22

Zeyde, K. M., M. V. Ronkin, and A. A. Kalmykov. "Electrodynamic Computer Model of a Metal Rod in a Concrete Medium Detection." Ural Radio Engineering Journal 5, no. 2 (2021): 104–18. http://dx.doi.org/10.15826/urej.2021.5.2.002.

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The main aim of the present work is to describe a generalized electrodynamic model of the specific device operation, which provides detection and measurement of the geometric characteristics of the reinforcement cage in a concrete structure. The result of this study is the design of the device’s receiving-transmitting path that is optimal in a number of parameters, as well as a signal processing algorithm based on the operation of an artificial neural network trained on the generalized computer model output data. In addition to the main functionality of the device being developed, which consists in structureroscopy by the method of radar holography, useful target characteristics may be obtained during its operation: electrophysical parameters of concrete, structural defects, visualization of an object, etc. To solve this problem, on the basis of general radar principles, frequency-modulated continuous wave was chosen as the operating mode of the device. To create an electrodynamic model, the computer-aided design environment Pathwave EM Design (EMPro) 2021 was used. The developed generalized model may be optimized for a large number of parameters. In addition to the position and number of receiving antennas, the list of optimization variables may include parameters of the transmitting antenna (ray width, directivity, near-field distance), their number (i.e., the capacity of the MIMO system), power on the transmitting side, etc. The proposed scheme of the device is presented as the main result.

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23

Yang, Bo, Selvaprabu Nadarajah, and Nicola Secomandi. "Pathwise Optimization for Merchant Energy Production." SSRN Electronic Journal, 2019. http://dx.doi.org/10.2139/ssrn.3510676.

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24

Schhssler, Rainer A., and Mark M. Trede. "Constructing Optimal Pathwise Confidence Bands Using Mixed-Integer Optimization." SSRN Electronic Journal, 2015. http://dx.doi.org/10.2139/ssrn.2701320.

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25

Levy, Daniel, and Stefano Ermon. "Deterministic Policy Optimization by Combining Pathwise and Score Function Estimators for Discrete Action Spaces." Proceedings of the AAAI Conference on Artificial Intelligence 32, no. 1 (April 29, 2018). http://dx.doi.org/10.1609/aaai.v32i1.11822.

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Policy optimization methods have shown great promise in solving complex reinforcement and imitation learning tasks. While model-free methods are broadly applicable, they often require many samples to optimize complex policies. Model-based methods greatly improve sample-efficiency but at the cost of poor generalization, requiring a carefully handcrafted model of the system dynamics for each task. Recently, hybrid methods have been successful in trading off applicability for improved sample-complexity. However, these have been limited to continuous action spaces. In this work, we present a new hybrid method based on an approximation of the dynamics as an expectation over the next state under the current policy. This relaxation allows us to derive a novel hybrid policy gradient estimator, combining score function and pathwise derivative estimators, that is applicable to discrete action spaces. We show significant gains in sample complexity, ranging between 1.7 and 25 times, when learning parameterized policies on Cart Pole, Acrobot, Mountain Car and Hand Mass. Our method is applicable to both discrete and continuous action spaces, when competing pathwise methods are limited to the latter.

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26

Yang, Bo, Selvaprabu Nadarajah, and Nicola Secomandi. "Least Squares Monte Carlo and Pathwise Optimization for Merchant Energy Production." SSRN Electronic Journal, 2021. http://dx.doi.org/10.2139/ssrn.3900797.

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27

Li, Jialin, and Ilya O. Ryzhov. "Convergence Rates of Epsilon-Greedy Global Optimization Under Radial Basis Function Interpolation." Stochastic Systems, August 2, 2022. http://dx.doi.org/10.1287/stsy.2022.0096.

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We study a global optimization problem where the objective function can be observed exactly at individual design points with no derivative information. We suppose that the design points are determined sequentially using an epsilon-greedy algorithm, that is, by sampling uniformly on the design space with a certain probability and otherwise sampling in a local neighborhood of the current estimate of the best solution. We study the rate at which the estimate converges to the global optimum and derive two types of bounds: an asymptotic pathwise rate and a concentration inequality measuring the likelihood that the asymptotic rate has not yet gone into effect. The order of the rate becomes faster when the width of the local search neighborhood is made to shrink over time at a suitably chosen speed.

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28

Bröcker, Jochen. "Existence and uniqueness for variational data assimilation in continuous time." Mathematical Control & Related Fields, 2021, 0. http://dx.doi.org/10.3934/mcrf.2021050.

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<p style='text-indent:20px;'>A variant of the optimal control problem is considered which is nonstandard in that the performance index contains "stochastic" integrals, that is, integrals against very irregular functions. The motivation for considering such performance indices comes from dynamical estimation problems where observed time series need to be "fitted" with trajectories of dynamical models. The observations may be contaminated with white noise, which gives rise to the nonstandard performance indices. Problems of this kind appear in engineering, physics, and the geosciences where this is referred to as data assimilation. The fact that typical models in the geosciences do not satisfy linear growth nor monotonicity conditions represents an additional difficulty. Pathwise existence of minimisers is obtained, along with a maximum principle as well as preliminary results in dynamic programming. The results also extend previous work on the maximum aposteriori estimator of trajectories of diffusion processes.</p>

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29

Yue, Jia, Ming-Hui Wang, Nan-Jing Huang, and Ben-zhang Yang. "Asset prices with investor protection and past information." Journal of Industrial and Management Optimization, 2022, 0. http://dx.doi.org/10.3934/jimo.2022062.

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<p style='text-indent:20px;'>In this paper, we consider a dynamic asset pricing model in an approximate fractional economy to address empirical regularities related to both investor protection and past information. Our newly developed model features not only a controlling shareholder who diverts a fraction of the output, but also good (or bad) memory in his budget dynamics which can be well-calibrated by a pathwise way from the historical data. We find that poorer investor protection leads to higher stock holdings of the controlling shareholder, lower gross stock returns, lower interest rates, and lower modified stock volatilities if the ownership concentration is sufficiently high. More importantly, by establishing an approximation scheme for good (bad) memory of investors on the historical market information, we conclude that good (bad) memory would increase (decrease) aforementioned dynamics and reveal that good (bad) memory strengthens (weakens) investor protection for the minority shareholder when the ownership concentration is sufficiently high, while good (bad) memory inversely weakens (strengthens) investor protection for the minority shareholder when the ownership concentration is sufficiently low. Our model's implications are consistent with a number of interesting facts documented in the recent literature.</p>

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30

Dhama, Shivam, and Chetan D. Pahlajani. "Approximation of linear controlled dynamical systems with small random noise and fast periodic sampling." Mathematical Control and Related Fields, 2022, 0. http://dx.doi.org/10.3934/mcrf.2022018.

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<p style='text-indent:20px;'>In this paper, we study the dynamics of a linear control system with given state feedback control law in the presence of fast periodic sampling at temporal frequency <inline-formula><tex-math id="M1">\begin{document}$ 1/\delta $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M2">\begin{document}$ 0 < \delta \ll 1 $\end{document}</tex-math></inline-formula>), together with small white noise perturbations of size <inline-formula><tex-math id="M3">\begin{document}$ \varepsilon $\end{document}</tex-math></inline-formula> (<inline-formula><tex-math id="M4">\begin{document}$ 0< \varepsilon \ll 1 $\end{document}</tex-math></inline-formula>) in the state dynamics. For the ensuing continuous-time stochastic process indexed by two small parameters <inline-formula><tex-math id="M5">\begin{document}$ \varepsilon,\delta $\end{document}</tex-math></inline-formula>, we obtain effective ordinary and stochastic differential equations describing the mean behavior and the typical fluctuations about the mean in the limit as <inline-formula><tex-math id="M6">\begin{document}$ \varepsilon,\delta \searrow 0 $\end{document}</tex-math></inline-formula>. The effective fluctuation process is found to vary, depending on whether <inline-formula><tex-math id="M7">\begin{document}$ \delta \searrow 0 $\end{document}</tex-math></inline-formula> faster than/at the same rate as/slower than <inline-formula><tex-math id="M8">\begin{document}$ \varepsilon \searrow 0 $\end{document}</tex-math></inline-formula>. The most interesting case is found to be the one where <inline-formula><tex-math id="M9">\begin{document}$ \delta, \varepsilon $\end{document}</tex-math></inline-formula> are comparable in size; here, the limiting stochastic differential equation for the fluctuations has both a diffusive term due to the small noise and an effective drift term which captures the cumulative effect of the fast sampling. In this regime, our results yield a time-inhomogeneous Markov process which provides a strong (pathwise) approximation of the original non-Markovian process, together with estimates on the ensuing error. A simple example involving an infinite time horizon linear quadratic regulation problem illustrates the results.</p>

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31

Lipshutz, David, and Kavita Ramanan. "Sensitivity Analysis for the Stationary Distribution of Reflected Brownian Motion in a Convex Polyhedral Cone." Mathematics of Operations Research, February 3, 2021. http://dx.doi.org/10.1287/moor.2020.1076.

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Reflected Brownian motion (RBM) in a convex polyhedral cone arises in a variety of applications ranging from the theory of stochastic networks to mathematical finance, and under general stability conditions, it has a unique stationary distribution. In such applications, to implement a stochastic optimization algorithm or quantify robustness of a model, it is useful to characterize the dependence of stationary performance measures on model parameters. In this paper, we characterize parametric sensitivities of the stationary distribution of an RBM in a simple convex polyhedral cone, that is, sensitivities to perturbations of the parameters that define the RBM—namely the covariance matrix, drift vector, and directions of reflection along the boundary of the polyhedral cone. In order to characterize these sensitivities, we study the long-time behavior of the joint process consisting of an RBM along with its so-called derivative process, which characterizes pathwise derivatives of RBMs on finite time intervals. We show that the joint process is positive recurrent and has a unique stationary distribution and that parametric sensitivities of the stationary distribution of an RBM can be expressed in terms of the stationary distribution of the joint process. This can be thought of as establishing an interchange of the differential operator and the limit in time. The analysis of ergodicity of the joint process is significantly more complicated than that of the RBM because of its degeneracy and the fact that the derivative process exhibits jumps that are modulated by the RBM. The proofs of our results rely on path properties of coupled RBMs and contraction properties related to the geometry of the polyhedral cone and directions of reflection along the boundary. Our results are potentially useful for developing efficient numerical algorithms for computing sensitivities of functionals of stationary RBMs.

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32

Kirk, Tanner, Richard Malak, and Raymundo Arroyave. "Computational Design of Compositionally Graded Alloys for Property Monotonicity." Journal of Mechanical Design 143, no. 3 (November 10, 2020). http://dx.doi.org/10.1115/1.4048627.

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Abstract Functionally graded materials (FGMs) exhibit spatial gradients in properties that can be exploited to satisfy multiple conflicting performance objectives in the same part. Compositionally graded alloys are a subclass of FGMs that have received increased attention with the development of metal additive manufacturing. However, the formation of secondary phases can often lead to cracks or deleterious properties in these materials. In prior work, a computational methodology was presented that can design compositional gradients to avoid these phases at any temperature without the need to visualize phase diagrams (Kirk et al., 2018, “Computational Design of Gradient Paths in Additively Manufactured Functionally Graded Materials,” ASME J. Mech. Des., 140(11), p. 111410). The methodology optimizes gradient paths through composition space for a specified cost function, but prior work only considered minimizing path length or maximizing the distance from undesirable phases. In this work, a new cost function is presented to produce compositional paths with optimal property gradients. Specifically, monotonicity is presented as the optimal quality of a pathwise property gradient because monotonic property gradients can be transformed to nearly any form on the part by controlling deposition rate. The proposed cost function uses a metric for non-monotonicity to find the shortest path with monotonic properties and is shown to be compatible with optimal path planners. A synthetic case study examines the effect of a cost function parameter on the trade-off between length and monotonicity. The cost function is also demonstrated in the Fe-Co-Cr system to find a compositional path with monotonic gradients in coefficient of thermal expansion (CTE). The deposition of the path on a hypothetical part is then planned subject to a maximum deposition rate and CTE gradient. Future work is proposed to extend the framework to optimize multiple properties at once and to incorporate multi-material topology optimization (MMTO) techniques into a complete design methodology for functionally graded metal parts.

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33

Zeyde, K. M., and D. S. Grishchenko. "Оn the experiment validity of the continuous medium motion detection by the waveguide method." Journal of Radio Electronics 2021, no. 1 (2021). http://dx.doi.org/10.30898/1684-1719.2021.8.5.

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Present work is devoted to the problem of validity increasing of an experiment to detect the motion of a continuous medium by the waveguide method. The study attempts to optimize the experiment to find the optimal scheme for its installation. The target effect, the magnitude of which should be maximum, is the generalized reflection coefficient, which is influenced by both the Fresnel electromagnetic drag coefficient and the polarization plane rotation due to motion of the medium. The main optimization task is to determine the output parameters for the experiment for stable and reliable motion detection of a continuous medium in a waveguide. In this work, a heuristic analysis algorithm is used. Optimization factors: frequency of the signal at microwave, physical dimensions of objects, shape of the waveguide cross-section, linear velocity of the medium. ECAD PathWave EM Design (EMPro) 2021 was used to the experiment designing stages. Distilled water is the moving medium, which is not subject to optimization. The motion of a continuous medium is considered through its refined refractive index. The maximum magnitude of the target effect is observed for the topology with a rectangular waveguide and with a tube oriented along a wide wall at f = [9.3 ÷ 9.5] GHz. These values coincide with a good degree of accuracy with the already conducted experiments.

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