Journal of Optimization Theory and Applications最新文献_第3页

Stochastic Augmented Lagrangian Method in Riemannian Shape Manifolds 黎曼形状芒模中的随机增量拉格朗日法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-21 DOI: 10.1007/s10957-024-02488-1

Caroline Geiersbach, Tim Suchan, Kathrin Welker

引用次数: 0

Regularized and Structured Tensor Total Least Squares Methods with Applications 正规化和结构化张量最小二乘法及其应用

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-12 DOI: 10.1007/s10957-024-02507-1

Feiyang Han, Yimin Wei, Pengpeng Xie

引用次数: 0

Continuous Equality Knapsack with Probit-Style Objectives 带有 Probit 类型目标的连续等价包

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-12 DOI: 10.1007/s10957-024-02503-5

Jamie Fravel, Robert Hildebrand, Laurel Travis

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Optimal Actuator Location of the Norm Optimal Controls for Degenerate Parabolic Equations 畸变抛物方程的规范最优控制的最佳执行器位置

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-06 DOI: 10.1007/s10957-024-02498-z

Yuanhang Liu, Weijia Wu, Donghui Yang

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Most Iterations of Projections Converge 大多数迭代预测趋于一致

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-05 DOI: 10.1007/s10957-024-02504-4

Daylen K. Thimm

{"title":"Most Iterations of Projections Converge","authors":"Daylen K. Thimm","doi":"10.1007/s10957-024-02504-4","DOIUrl":"https://doi.org/10.1007/s10957-024-02504-4","url":null,"abstract":"Consider three closed linear subspaces (C_1, C_2,) and (C_3) of a Hilbert space H and the orthogonal projections (P_1, P_2) and (P_3) onto them. Halperin showed that a point in (C_1cap C_2 cap C_3) can be found by iteratively projecting any point (x_0 in H) onto all the sets in a periodic fashion. The limit point is then the projection of (x_0) onto (C_1cap C_2 cap C_3). Nevertheless, a non-periodic projection order may lead to a non-convergent projection series, as shown by Kopecká, Müller, and Paszkiewicz. This raises the question how many projection orders in ({1,2,3}^{mathbb {N}}) are “well behaved” in the sense that they lead to a convergent projection series. Melo, da Cruz Neto, and de Brito provided a necessary and sufficient condition under which the projection series converges and showed that the “well behaved” projection orders form a large subset in the sense of having full product measure. We show that also from a topological viewpoint the set of “well behaved” projection orders is a large subset: it contains a dense (G_delta ) subset with respect to the product topology. Furthermore, we analyze why the proof of the measure theoretic case cannot be directly adapted to the topological setting.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"9 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141935102","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

Specifying and Solving Robust Empirical Risk Minimization Problems Using CVXPY 使用 CVXPY 指定和解决稳健经验风险最小化问题

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-04 DOI: 10.1007/s10957-024-02491-6

Eric Luxenberg, Dhruv Malik, Yuanzhi Li, Aarti Singh, Stephen Boyd

引用次数: 0

Convergence Analysis of a New Forward-Reflected-Backward Algorithm for Four Operators Without Cocoercivity 四算子无矫顽力新正向-反射-后向算法的收敛性分析

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-02 DOI: 10.1007/s10957-024-02501-7

Yu Cao, Yuanheng Wang, Habib ur Rehman, Yekini Shehu, Jen-Chih Yao

引用次数: 0

Variance Reduction Techniques for Stochastic Proximal Point Algorithms 随机近点算法的方差缩小技术

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-02 DOI: 10.1007/s10957-024-02502-6

Cheik Traoré, Vassilis Apidopoulos, Saverio Salzo, Silvia Villa

{"title":"Variance Reduction Techniques for Stochastic Proximal Point Algorithms","authors":"Cheik Traoré, Vassilis Apidopoulos, Saverio Salzo, Silvia Villa","doi":"10.1007/s10957-024-02502-6","DOIUrl":"https://doi.org/10.1007/s10957-024-02502-6","url":null,"abstract":"In the context of finite sums minimization, variance reduction techniques are widely used to improve the performance of state-of-the-art stochastic gradient methods. Their practical impact is clear, as well as their theoretical properties. Stochastic proximal point algorithms have been studied as an alternative to stochastic gradient algorithms since they are more stable with respect to the choice of the step size. However, their variance-reduced versions are not as well studied as the gradient ones. In this work, we propose the first unified study of variance reduction techniques for stochastic proximal point algorithms. We introduce a generic stochastic proximal-based algorithm that can be specified to give the proximal version of SVRG, SAGA, and some of their variants. For this algorithm, in the smooth setting, we provide several convergence rates for the iterates and the objective function values, which are faster than those of the vanilla stochastic proximal point algorithm. More specifically, for convex functions, we prove a sublinear convergence rate of O(1/k). In addition, under the Polyak-łojasiewicz condition, we obtain linear convergence rates. Finally, our numerical experiments demonstrate the advantages of the proximal variance reduction methods over their gradient counterparts in terms of the stability with respect to the choice of the step size in most cases, especially for difficult problems.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"5 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882639","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 Method for Multi-Leader–Multi-Follower Games by Smoothing the Followers’ Response Function 通过平滑追随者的响应函数实现多领导者与多追随者博弈的方法

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-02 DOI: 10.1007/s10957-024-02506-2

Atsushi Hori, Daisuke Tsuyuguchi, Ellen H. Fukuda

{"title":"A Method for Multi-Leader–Multi-Follower Games by Smoothing the Followers’ Response Function","authors":"Atsushi Hori, Daisuke Tsuyuguchi, Ellen H. Fukuda","doi":"10.1007/s10957-024-02506-2","DOIUrl":"https://doi.org/10.1007/s10957-024-02506-2","url":null,"abstract":"The multi-leader–multi-follower game (MLMFG) involves two or more leaders and followers and serves as a generalization of the Stackelberg game and the single-leader–multi-follower game. Although MLMFG covers wide range of real-world applications, its research is still sparse. Notably, fundamental solution methods for this class of problems remain insufficiently established. A prevailing approach is to recast the MLMFG as an equilibrium problem with equilibrium constraints (EPEC) and solve it using a solver. Meanwhile, interpreting the solution to the EPEC in the context of MLMFG may be complex due to shared decision variables among all leaders, followers’ strategies that each leader can unilaterally change, but the variables are essentially controlled by followers. To address this issue, we introduce a response function of followers’ noncooperative game that is a function with leaders’ strategies as a variable. Employing this approach allows the MLMFG to be solved as a single-level differentiable variational inequality using a smoothing scheme for the followers’ response function. We also demonstrate that the sequence of solutions to the smoothed variational inequality converges to a stationary equilibrium of the MLMFG. Finally, we illustrate the behavior of the smoothing method by numerical experiments.","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"22 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882506","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

Pontryagin’s Maximum Principle for a State-Constrained System of Douglis-Nirenberg Type 道格里斯-尼伦伯格类型状态受限系统的庞特里亚金最大原则

IF 1.9 3区数学

Journal of Optimization Theory and Applications Pub Date : 2024-08-01 DOI: 10.1007/s10957-024-02499-y

Alexey S. Matveev, Dmitrii V. Sugak

{"title":"Pontryagin’s Maximum Principle for a State-Constrained System of Douglis-Nirenberg Type","authors":"Alexey S. Matveev, Dmitrii V. Sugak","doi":"10.1007/s10957-024-02499-y","DOIUrl":"https://doi.org/10.1007/s10957-024-02499-y","url":null,"abstract":"This article is concerned with optimal control problems for plants described by systems of high order nonlinear PDE’s (whose linear approximation is elliptic in the sense of Douglis-Nirenberg), with a special attention being given to their particular case: the standard stationary system of non-linear Navier–Stokes equations. The objective is to establish an analog of the Pontryagin’s maximum principle. The major challenge stems from the presence of infinitely many point-wise constraints on the system’s state, which are imposed at any point from a given continuum set of independent variables. Necessary conditions for optimality in the form of an “abstract” maximum principle are first obtained for a general optimal control problem couched in the language of functional analysis. This result is targeted at a wide class of problems, with an idea to absorb, in its proof, a great deal of technical work needed for derivation of optimality conditions so that only an interpretation of the discussed result would be basically needed to handle a particular problem. The applicability of this approach is demonstrated via obtaining the afore-mentioned analog of the Pontryagin’s maximum principle for a state-constrained system of high-order elliptic equations and the Navier–Stokes equations.\u0000","PeriodicalId":50100,"journal":{"name":"Journal of Optimization Theory and Applications","volume":"4 1","pages":""},"PeriodicalIF":1.9,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141882505","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