SIAM Journal on Optimization最新文献_第2页

Data-Driven Distributionally Robust Multiproduct Pricing Problems under Pure Characteristics Demand Models 纯特征需求模型下数据驱动的分布稳健型多产品定价问题

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-09-03 DOI: 10.1137/23m1585131

Jie Jiang, Hailin Sun, Xiaojun Chen

{"title":"Data-Driven Distributionally Robust Multiproduct Pricing Problems under Pure Characteristics Demand Models","authors":"Jie Jiang, Hailin Sun, Xiaojun Chen","doi":"10.1137/23m1585131","DOIUrl":"https://doi.org/10.1137/23m1585131","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2917-2942, September 2024. Abstract. This paper considers a multiproduct pricing problem under pure characteristics demand models when the probability distribution of the random parameter in the problem is uncertain. We formulate this problem as a distributionally robust optimization (DRO) problem based on a constructive approach to estimating pure characteristics demand models with pricing by Pang, Su, and Lee. In this model, the consumers’ purchase decision is to maximize their utility. We show that the DRO problem is well-defined, and the objective function is upper semicontinuous by using an equivalent hierarchical form. We also use the data-driven approach to analyze the DRO problem when the ambiguity set, i.e., a set of probability distributions that contains some exact information of the underlying probability distribution, is given by a general moment-based case. We give convergence results as the data size tends to infinity and analyze the quantitative statistical robustness in view of the possible contamination of driven data. Furthermore, we use the Lagrange duality to reformulate the DRO problem as a mathematical program with complementarity constraints, and give a numerical procedure for finding a global solution of the DRO problem under certain specific settings. Finally, we report numerical results that validate the effectiveness and scalability of our approach for the distributionally robust multiproduct pricing problem.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"47 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212459","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

MIP Relaxations in Factorable Programming 可因式编程中的 MIP 放松

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-08-26 DOI: 10.1137/22m1515537

Taotao He, Mohit Tawarmalani

引用次数: 0

On a Differential Generalized Nash Equilibrium Problem with Mean Field Interaction 论具有平均场相互作用的差分广义纳什均衡问题

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-08-23 DOI: 10.1137/22m1489952

Michael Hintermüller, Thomas M. Surowiec, Mike Theiß

{"title":"On a Differential Generalized Nash Equilibrium Problem with Mean Field Interaction","authors":"Michael Hintermüller, Thomas M. Surowiec, Mike Theiß","doi":"10.1137/22m1489952","DOIUrl":"https://doi.org/10.1137/22m1489952","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2821-2855, September 2024. Abstract. We consider a class of [math]-player linear quadratic differential generalized Nash equilibrium problems (GNEPs) with bound constraints on the individual control and state variables. In addition, we assume the individual players’ optimal control problems are coupled through their dynamics and objectives via a time-dependent mean field interaction term. This assumption allows us to model the realistic setting that strategic players in large games cannot observe the individual states of their competitors. We observe that the GNEPs require a constraint qualification, which necessitates sufficient robustness of the individuals, in order to prove the existence of an open-loop pure strategy Nash equilibrium and to derive optimality conditions. In order to gain qualitative insight into the [math]-player game, we assume that players are identical and pass to the limit in [math] to derive a type of first-order constrained mean field game (MFG). We prove that the mean field interaction terms converge to an absolutely continuous curve of probability measures on the set of possible state trajectories. Using variational convergence methods, we show that the optimal control problems converge to a representative agent problem. Under additional regularity assumptions, we provide an explicit form for the mean field term as the solution of a continuity equation and demonstrate the link back to the [math]-player GNEP.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"25 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212462","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

MGProx: A Nonsmooth Multigrid Proximal Gradient Method with Adaptive Restriction for Strongly Convex Optimization MGProx：用于强凸优化的带有自适应限制的非光滑多网格近端梯度法

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-08-13 DOI: 10.1137/23m1552140

Andersen Ang, Hans De Sterck, Stephen Vavasis

{"title":"MGProx: A Nonsmooth Multigrid Proximal Gradient Method with Adaptive Restriction for Strongly Convex Optimization","authors":"Andersen Ang, Hans De Sterck, Stephen Vavasis","doi":"10.1137/23m1552140","DOIUrl":"https://doi.org/10.1137/23m1552140","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2788-2820, September 2024. Abstract. We study the combination of proximal gradient descent with multigrid for solving a class of possibly nonsmooth strongly convex optimization problems. We propose a multigrid proximal gradient method called MGProx, which accelerates the proximal gradient method by multigrid, based on using hierarchical information of the optimization problem. MGProx applies a newly introduced adaptive restriction operator to simplify the Minkowski sum of subdifferentials of the nondifferentiable objective function across different levels. We provide a theoretical characterization of MGProx. First we show that the MGProx update operator exhibits a fixed-point property. Next, we show that the coarse correction is a descent direction for the fine variable of the original fine level problem in the general nonsmooth case. Last, under some assumptions we provide the convergence rate for the algorithm. In the numerical tests on the elastic obstacle problem, which is an example of a nonsmooth convex optimization problem where the multigrid method can be applied, we show that MGProx has a faster convergence speed than competing methods.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"33 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-08-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142212474","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

Variational and Strong Variational Convexity in Infinite-Dimensional Variational Analysis 无穷维变分分析中的变分凸性和强变分凸性

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-08-12 DOI: 10.1137/23m1604667

P. D. Khanh, V. V. H. Khoa, B. S. Mordukhovich, V. T. Phat

引用次数: 0

Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation 采用线性函数逼近的熵细化自然策略梯度的收敛性

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-07-30 DOI: 10.1137/22m1540156

Semih Cayci, Niao He, R. Srikant

{"title":"Convergence of Entropy-Regularized Natural Policy Gradient with Linear Function Approximation","authors":"Semih Cayci, Niao He, R. Srikant","doi":"10.1137/22m1540156","DOIUrl":"https://doi.org/10.1137/22m1540156","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2729-2755, September 2024. Abstract. Natural policy gradient (NPG) methods, equipped with function approximation and entropy regularization, achieve impressive empirical success in reinforcement learning problems with large state-action spaces. However, their convergence properties and the impact of entropy regularization remain elusive in the function approximation regime. In this paper, we establish finite-time convergence analyses of entropy-regularized NPG with linear function approximation under softmax parameterization. In particular, we prove that entropy-regularized NPG with averaging satisfies the persistence of excitation condition, and achieves a fast convergence rate of [math] up to a function approximation error in regularized Markov decision processes. This convergence result does not require any a priori assumptions on the policies. Furthermore, under mild regularity conditions on the concentrability coefficient and basis vectors, we prove that entropy-regularized NPG exhibits linear convergence up to the compatible function approximation error. Finally, we provide sample complexity results for sample-based NPG with entropy regularization.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"171 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141863905","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

Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses 随机子空间中的随机信任区域算法及收敛性和预期复杂性分析

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-07-25 DOI: 10.1137/22m1524072

K. J. Dzahini, S. M. Wild

{"title":"Stochastic Trust-Region Algorithm in Random Subspaces with Convergence and Expected Complexity Analyses","authors":"K. J. Dzahini, S. M. Wild","doi":"10.1137/22m1524072","DOIUrl":"https://doi.org/10.1137/22m1524072","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2671-2699, September 2024. Abstract. This work proposes a framework for large-scale stochastic derivative-free optimization (DFO) by introducing STARS, a trust-region method based on iterative minimization in random subspaces. This framework is both an algorithmic and theoretical extension of a random subspace derivative-free optimization (RSDFO) framework, and an algorithm for stochastic optimization with random models (STORM). Moreover, like RSDFO, STARS achieves scalability by minimizing interpolation models that approximate the objective in low-dimensional affine subspaces, thus significantly reducing per-iteration costs in terms of function evaluations and yielding strong performance on large-scale stochastic DFO problems. The user-determined dimension of these subspaces, when the latter are defined, for example, by the columns of so-called Johnson–Lindenstrauss transforms, turns out to be independent of the dimension of the problem. For convergence purposes, inspired by the analyses of RSDFO and STORM, both a particular quality of the subspace and the accuracies of random function estimates and models are required to hold with sufficiently high, but fixed, probabilities. Using martingale theory under the latter assumptions, an almost sure global convergence of STARS to a first-order stationary point is shown, and the expected number of iterations required to reach a desired first-order accuracy is proved to be similar to that of STORM and other stochastic DFO algorithms, up to constants.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"68 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-07-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141775205","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

Convergence Analysis of a Norm Minimization-Based Convex Vector Optimization Algorithm 基于规范最小化的凸向量优化算法的收敛性分析

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-07-25 DOI: 10.1137/23m1574580

Çağin Ararat, Firdevs Ulus, Muhammad Umer

引用次数: 0

Small Errors in Random Zeroth-Order Optimization Are Imaginary 随机零阶优化中的小误差是虚构的

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-07-19 DOI: 10.1137/22m1510261

Wouter Jongeneel, Man-Chung Yue, Daniel Kuhn

{"title":"Small Errors in Random Zeroth-Order Optimization Are Imaginary","authors":"Wouter Jongeneel, Man-Chung Yue, Daniel Kuhn","doi":"10.1137/22m1510261","DOIUrl":"https://doi.org/10.1137/22m1510261","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2638-2670, September 2024. Abstract. Most zeroth-order optimization algorithms mimic a first-order algorithm but replace the gradient of the objective function with some gradient estimator that can be computed from a small number of function evaluations. This estimator is constructed randomly, and its expectation matches the gradient of a smooth approximation of the objective function whose quality improves as the underlying smoothing parameter [math] is reduced. Gradient estimators requiring a smaller number of function evaluations are preferable from a computational point of view. While estimators based on a single function evaluation can be obtained by use of the divergence theorem from vector calculus, their variance explodes as [math] tends to 0. Estimators based on multiple function evaluations, on the other hand, suffer from numerical cancellation when [math] tends to 0. To combat both effects simultaneously, we extend the objective function to the complex domain and construct a gradient estimator that evaluates the objective at a complex point whose coordinates have small imaginary parts of the order [math]. As this estimator requires only one function evaluation, it is immune to cancellation. In addition, its variance remains bounded as [math] tends to 0. We prove that zeroth-order algorithms that use our estimator offer the same theoretical convergence guarantees as the state-of-the-art methods. Numerical experiments suggest, however, that they often converge faster in practice.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"80 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141738174","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

Square Root LASSO: Well-Posedness, Lipschitz Stability, and the Tuning Trade-Off 平方根 LASSO：拟合性、Lipschitz 稳定性和调整权衡

IF 3.1 1区数学

SIAM Journal on Optimization Pub Date : 2024-07-18 DOI: 10.1137/23m1561968

Aaron Berk, Simone Brugiapaglia, Tim Hoheisel

{"title":"Square Root LASSO: Well-Posedness, Lipschitz Stability, and the Tuning Trade-Off","authors":"Aaron Berk, Simone Brugiapaglia, Tim Hoheisel","doi":"10.1137/23m1561968","DOIUrl":"https://doi.org/10.1137/23m1561968","url":null,"abstract":"SIAM Journal on Optimization, Volume 34, Issue 3, Page 2609-2637, September 2024. Abstract. This paper studies well-posedness and parameter sensitivity of the square root LASSO (SR-LASSO), an optimization model for recovering sparse solutions to linear inverse problems in finite dimension. An advantage of the SR-LASSO (e.g., over the standard LASSO) is that the optimal tuning of the regularization parameter is robust with respect to measurement noise. This paper provides three point-based regularity conditions at a solution of the SR-LASSO: the weak, intermediate, and strong assumptions. It is shown that the weak assumption implies uniqueness of the solution in question. The intermediate assumption yields a directionally differentiable and locally Lipschitz solution map (with explicit Lipschitz bounds), whereas the strong assumption gives continuous differentiability of said map around the point in question. Our analysis leads to new theoretical insights on the comparison between SR-LASSO and LASSO from the viewpoint of tuning parameter sensitivity: noise-robust optimal parameter choice for SR-LASSO comes at the “price” of elevated tuning parameter sensitivity. Numerical results support and showcase the theoretical findings.","PeriodicalId":49529,"journal":{"name":"SIAM Journal on Optimization","volume":"22 1","pages":""},"PeriodicalIF":3.1,"publicationDate":"2024-07-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141745955","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