SIAM Journal on Optimization最新文献_第10页

Exact Quantization of Multistage Stochastic Linear Problems 多阶段随机线性问题的精确量化

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-05 DOI: 10.1137/22m1508005

Maël Forcier, Stéphane Gaubert, Vincent Leclère

引用次数: 0

Hybrid Algorithms for Finding a D-Stationary Point of a Class of Structured Nonsmooth DC Minimization 寻找一类结构非光滑直流最小化的 D-静态点的混合算法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-01 DOI: 10.1137/21m1457709

Zhe Sun, Lei Wu

引用次数: 0

Shortest Paths in Graphs of Convex Sets 凸集合图中的最短路径

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-02-01 DOI: 10.1137/22m1523790

Tobia Marcucci, Jack Umenberger, Pablo Parrilo, Russ Tedrake

引用次数: 0

Infeasibility Detection with Primal-Dual Hybrid Gradient for Large-Scale Linear Programming 大规模线性规划的原点-双混合梯度不可行性检测

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-31 DOI: 10.1137/22m1510467

David Applegate, Mateo Díaz, Haihao Lu, Miles Lubin

{"title":"Infeasibility Detection with Primal-Dual Hybrid Gradient for Large-Scale Linear Programming","authors":"David Applegate, Mateo Díaz, Haihao Lu, Miles Lubin","doi":"10.1137/22m1510467","DOIUrl":"https://doi.org/10.1137/22m1510467","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 459-484, March 2024. <br/> Abstract. We study the problem of detecting infeasibility of large-scale linear programming problems using the primal-dual hybrid gradient (PDHG) method of Chambolle and Pock [J. Math. Imaging Vision, 40 (2011), pp. 120–145]. The literature on PDHG has focused chiefly on problems with at least one optimal solution. We show that when the problem is infeasible or unbounded, the iterates diverge at a controlled rate toward a well-defined ray. In turn, the direction of such a ray recovers infeasibility certificates. Based on this fact, we propose a simple way to extract approximate infeasibility certificates from the iterates of PDHG. We study three sequences that converge to certificates: the difference of iterates, the normalized iterates, and the normalized average. All of them are easy to compute and suitable for large-scale problems. We show that the normalized iterates and normalized averages achieve a convergence rate of [math]. This rate is general and applies to any fixed-point iteration of a nonexpansive operator. Thus, it is a result of independent interest that goes well beyond our setting. Finally, we show that, under nondegeneracy assumptions, the iterates of PDHG identify the active set of an auxiliary feasible problem in finite time, which ensures that the difference of iterates exhibits eventual linear convergence. These results provide a theoretical justification for infeasibility detection in the newly developed linear programming solver PDLP.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"26 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139657357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Distributionally Favorable Optimization: A Framework for Data-Driven Decision-Making with Endogenous Outliers 有利于分布的优化：内生异常值数据驱动决策框架

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-29 DOI: 10.1137/22m1528094

Nan Jiang, Weijun Xie

{"title":"Distributionally Favorable Optimization: A Framework for Data-Driven Decision-Making with Endogenous Outliers","authors":"Nan Jiang, Weijun Xie","doi":"10.1137/22m1528094","DOIUrl":"https://doi.org/10.1137/22m1528094","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 419-458, March 2024. <br/> Abstract. A typical data-driven stochastic program seeks the best decision that minimizes the sum of a deterministic cost function and an expected recourse function under a given distribution. Recently, much success has been witnessed in the development of distributionally robust optimization (DRO), which considers the worst-case expected recourse function under the least favorable probability distribution from a distributional family. However, in the presence of endogenous outliers such that their corresponding recourse function values are very large or even infinite, the commonly used DRO framework alone tends to overemphasize these endogenous outliers and cause undesirable or even infeasible decisions. On the contrary, distributionally favorable optimization (DFO), concerning the best-case expected recourse function under the most favorable distribution from the distributional family, can serve as a proper measure of the stochastic recourse function and mitigate the effect of endogenous outliers. We show that DFO recovers many robust statistics, suggesting that the DFO framework might be appropriate for the stochastic recourse function in the presence of endogenous outliers. A notion of decision outlier robustness is proposed for selecting a DFO framework for data-driven optimization with outliers. We also provide a unified way to integrate DRO with DFO, where DRO addresses the out-of-sample performance, and DFO properly handles the stochastic recourse function under endogenous outliers. We further extend the proposed DFO framework to solve two-stage stochastic programs without relatively complete recourse. The numerical study demonstrates that the framework is promising.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"46 2 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139585526","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Bayesian Stochastic Gradient Descent for Stochastic Optimization with Streaming Input Data 利用流输入数据进行随机优化的贝叶斯随机梯度下降法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-25 DOI: 10.1137/22m1478951

Tianyi Liu, Yifan Lin, Enlu Zhou

引用次数: 0

Descent Properties of an Anderson Accelerated Gradient Method with Restarting 带重启的安德森加速梯度法的下降特性

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-19 DOI: 10.1137/22m151460x

Wenqing Ouyang, Yang Liu, Andre Milzarek

引用次数: 0

Basic Convex Analysis in Metric Spaces with Bounded Curvature 有界曲率公元空间中的基本凸分析

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-19 DOI: 10.1137/23m1551389

Adrian S. Lewis, Genaro López-Acedo, Adriana Nicolae

引用次数: 0

A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse Functions 具有非凸求助函数的两阶段随机程序的分解算法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-19 DOI: 10.1137/22m1488533

Hanyang Li, Ying Cui

{"title":"A Decomposition Algorithm for Two-Stage Stochastic Programs with Nonconvex Recourse Functions","authors":"Hanyang Li, Ying Cui","doi":"10.1137/22m1488533","DOIUrl":"https://doi.org/10.1137/22m1488533","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 306-335, March 2024. <br/> Abstract. In this paper, we have studied a decomposition method for solving a class of nonconvex two-stage stochastic programs, where both the objective and constraints of the second-stage problem are nonlinearly parameterized by the first-stage variables. Due to the failure of the Clarke regularity of the resulting nonconvex recourse function, classical decomposition approaches such as Benders decomposition and (augmented) Lagrangian-based algorithms cannot be directly generalized to solve such models. By exploring an implicitly convex-concave structure of the recourse function, we introduce a novel decomposition framework based on the so-called partial Moreau envelope. The algorithm successively generates strongly convex quadratic approximations of the recourse function based on the solutions of the second-stage convex subproblems and adds them to the first-stage master problem. Convergence has been established for both a fixed number of scenarios and a sequential internal sampling strategy. Numerical experiments are conducted to demonstrate the effectiveness of the proposed algorithm.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"1 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495101","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Sharper Bounds for Proximal Gradient Algorithms with Errors 有误差的近端梯度算法的更清晰边界

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-01-19 DOI: 10.1137/22m1480161

Anis Hamadouche, Yun Wu, Andrew M. Wallace, João F. C. Mota

{"title":"Sharper Bounds for Proximal Gradient Algorithms with Errors","authors":"Anis Hamadouche, Yun Wu, Andrew M. Wallace, João F. C. Mota","doi":"10.1137/22m1480161","DOIUrl":"https://doi.org/10.1137/22m1480161","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 1, Page 278-305, March 2024. <br/> Abstract. We analyze the convergence of the proximal gradient algorithm for convex composite problems in the presence of gradient and proximal computational inaccuracies. We generalize the deterministic analysis to the quasi-Fejér case and quantify the uncertainty incurred from approximate computing and early termination errors. We propose new probabilistic tighter bounds that we use to verify a simulated Model Predictive Control (MPC) with sparse controls problem solved with early termination, reduced precision, and proximal errors. We also show how the probabilistic bounds are more suitable than the deterministic ones for algorithm verification and more accurate for application performance guarantees. Under mild statistical assumptions, we also prove that some cumulative error terms follow a martingale property. And conforming to observations, e.g., in [M. Schmidt, N. L. Roux, and F. R. Bach, Convergence rates of inexact proximal-gradient methods for convex optimization, in Advances in Neural Information Processing Systems, 2011, pp. 1458–1466], we also show how the acceleration of the algorithm amplifies the gradient and proximal computational errors.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"27 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139495041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0