Journal of Optimization Theory and Applications最新文献_第8页

Exterior-Point Optimization for Sparse and Low-Rank Optimization 稀疏和低域优化的外点优化

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-26 DOI: 10.1007/s10957-024-02448-9

Shuvomoy Das Gupta, Bartolomeo Stellato, Bart P. G. Van Parys

{"title":"Exterior-Point Optimization for Sparse and Low-Rank Optimization","authors":"Shuvomoy Das Gupta, Bartolomeo Stellato, Bart P. G. Van Parys","doi":"10.1007/s10957-024-02448-9","DOIUrl":"https://doi.org/10.1007/s10957-024-02448-9","url":null,"abstract":"Many problems of substantial current interest in machine learning, statistics, and data science can be formulated as sparse and low-rank optimization problems. In this paper, we present the nonconvex exterior-point optimization solver (NExOS)—a first-order algorithm tailored to sparse and low-rank optimization problems. We consider the problem of minimizing a convex function over a nonconvex constraint set, where the set can be decomposed as the intersection of a compact convex set and a nonconvex set involving sparse or low-rank constraints. Unlike the convex relaxation approaches, NExOS finds a locally optimal point of the original problem by solving a sequence of penalized problems with strictly decreasing penalty parameters by exploiting the nonconvex geometry. NExOS solves each penalized problem by applying a first-order algorithm, which converges linearly to a local minimum of the corresponding penalized formulation under regularity conditions. Furthermore, the local minima of the penalized problems converge to a local minimum of the original problem as the penalty parameter goes to zero. We then implement and test NExOS on many instances from a wide variety of sparse and low-rank optimization problems, empirically demonstrating that our algorithm outperforms specialized methods.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"84 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141171300","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Stabilizability for Quasilinear Klein–Gordon–Schrödinger System with Variable Coefficients 具有可变系数的准线性克莱因-戈登-薛定谔系统的稳定性

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-25 DOI: 10.1007/s10957-024-02445-y

Weijia Li, Yuqi Shangguan, Weiping Yan

引用次数: 0

Rigidity Results for the p-Laplacian Poisson Problem with Robin Boundary Conditions 带罗宾边界条件的 p 拉普拉斯泊松问题的刚性结果

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-14 DOI: 10.1007/s10957-024-02442-1

Alba Lia Masiello, Gloria Paoli

引用次数: 0

Periodic Optimal Control of a Plug Flow Reactor Model with an Isoperimetric Constraint 具有等容约束条件的塞流反应器模型的周期性优化控制

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-14 DOI: 10.1007/s10957-024-02439-w

Yevgeniia Yevgenieva, Alexander Zuyev, Peter Benner, Andreas Seidel-Morgenstern

引用次数: 0

Robust Bond Portfolio Construction via Convex–Concave Saddle Point Optimization 通过凸凹鞍点优化构建稳健的债券投资组合

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-13 DOI: 10.1007/s10957-024-02436-z

Eric Luxenberg, Philipp Schiele, Stephen Boyd

引用次数: 0

Perturbation Analysis on T-Eigenvalues of Third-Order Tensors 三阶张量 T 特征值的扰动分析

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-10 DOI: 10.1007/s10957-024-02444-z

Changxin Mo, Weiyang Ding, Yimin Wei

{"title":"Perturbation Analysis on T-Eigenvalues of Third-Order Tensors","authors":"Changxin Mo, Weiyang Ding, Yimin Wei","doi":"10.1007/s10957-024-02444-z","DOIUrl":"https://doi.org/10.1007/s10957-024-02444-z","url":null,"abstract":"This paper concentrates on perturbation theory concerning the tensor T-eigenvalues within the framework of tensor-tensor multiplication. Notably, it serves as a cornerstone for the extension of semidefinite programming into the domain of tensor fields, referred to as T-semidefinite programming. The analytical perturbation analysis delves into the sensitivity of T-eigenvalues for third-order tensors with square frontal slices, marking the first main part of this study. Three classical results from the matrix domain into the tensor domain are extended. Firstly, this paper presents the Gershgorin disc theorem for tensors, demonstrating the confinement of all T-eigenvalues within a union of Gershgorin discs. Afterward, generalizations of the Bauer-Fike theorem are provided, each applicable to different cases involving tensors, including those that are F-diagonalizable and those that are not. Lastly, the Kahan theorem is presented, addressing the perturbation of a Hermite tensor by any tensors. Additionally, the analysis establishes connections between the T-eigenvalue problem and various optimization problems. The second main part of the paper focuses on tensor pseudospectra theory, presenting four equivalent definitions to characterize tensor (varepsilon )-pseudospectra. Accompanied by a thorough analysis of their properties and illustrative visualizations, this section also explores the application of tensor (varepsilon )-pseudospectra in identifying more T-positive definite tensors.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"19 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Robust Risk Management via Multi-marginal Optimal Transport 通过多边际优化运输实现稳健风险管理

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-09 DOI: 10.1007/s10957-024-02438-x

Hamza Ennaji, Quentin Mérigot, Luca Nenna, Brendan Pass

{"title":"Robust Risk Management via Multi-marginal Optimal Transport","authors":"Hamza Ennaji, Quentin Mérigot, Luca Nenna, Brendan Pass","doi":"10.1007/s10957-024-02438-x","DOIUrl":"https://doi.org/10.1007/s10957-024-02438-x","url":null,"abstract":"We study the problem of maximizing a spectral risk measure of a given output function which depends on several underlying variables, whose individual distributions are known but whose joint distribution is not. We establish and exploit an equivalence between this problem and a multi-marginal optimal transport problem. We use this reformulation to establish explicit, closed form solutions when the underlying variables are one dimensional, for a large class of output functions. For higher dimensional underlying variables, we identify conditions on the output function and marginal distributions under which solutions concentrate on graphs over the first variable and are unique, and, for general output functions, we find upper bounds on the dimension of the support of the solution. We also establish a stability result on the maximal value and maximizing joint distributions when the output function, marginal distributions and spectral function are perturbed; in addition, when the variables one dimensional, we show that the optimal value exhibits Lipschitz dependence on the marginal distributions for a certain class of output functions. Finally, we show that the equivalence to a multi-marginal optimal transport problem extends to maximal correlation measures of multi-dimensional risks; in this setting, we again establish conditions under which the solution concentrates on a graph over the first marginal.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"59 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140925256","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium 选择完美平衡的逻辑数量反应平衡变体

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-05-03 DOI: 10.1007/s10957-024-02433-2

Yiyin Cao, Yin Chen, Chuangyin Dang

{"title":"A Variant of the Logistic Quantal Response Equilibrium to Select a Perfect Equilibrium","authors":"Yiyin Cao, Yin Chen, Chuangyin Dang","doi":"10.1007/s10957-024-02433-2","DOIUrl":"https://doi.org/10.1007/s10957-024-02433-2","url":null,"abstract":"The concept of perfect equilibrium, formulated by Selten (Int J Game Theory 4:25–55, 1975), serves as an effective characterization of rationality in strategy perturbation. In our study, we propose a modified version of perfect equilibrium that incorporates perturbation control parameters. To match the beliefs with the equilibrium choice probabilities, the logistic quantal response equilibrium (logistic QRE) was established by McKelvey and Palfrey (Games Econ Behav 10:6–38, 1995), which is only able to select a Nash equilibrium. By introducing a linear combination between a mixed strategy profile and a given vector with positive elements, this paper develops a variant of the logistic QRE for the selection of the special version of perfect equilibrium. Expanding upon this variant, we construct an equilibrium system that incorporates an exponential function of an extra variable. Through rigorous error-bound analysis, we demonstrate that the solution set of this equilibrium system leads to a perfect equilibrium as the extra variable approaches zero. Consequently, we establish the existence of a smooth path to a perfect equilibrium and employ an exponential transformation of variables to ensure numerical stability. To make a numerical comparison, we capitalize on a variant of the square-root QRE, which yields another smooth path to a perfect equilibrium. Numerical results further verify the effectiveness and efficiency of the proposed differentiable path-following methods.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"25 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-05-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140889265","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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

Local Boundedness for Minimizers of Anisotropic Functionals with Monomial Weights 具有单项权重的各向异性函数最小化的局部有界性

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-04-29 DOI: 10.1007/s10957-024-02432-3

Filomena Feo, Antonia Passarelli di Napoli, Maria Rosaria Posteraro

引用次数: 0

An Efficient GIPM Algorithm for Computing the Smallest V-Singular Value of the Partially Symmetric Tensor 计算部分对称张量最小 V 星形值的高效 GIPM 算法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-04-26 DOI: 10.1007/s10957-024-02434-1

Zhuolin Du, Chunyan Wang, Haibin Chen, Hong Yan

引用次数: 0