无穷维凸优化问题的单投影程序

IF 2.6 1区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Optimization Pub Date : 2024-05-03 DOI:10.1137/22m1530173

Hoa T. Bui, Regina S. Burachik, Evgeni A. Nurminski, Matthew K. Tam

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引用次数: 0

摘要

SIAM 优化期刊》第 34 卷第 2 期第 1646-1678 页，2024 年 6 月。摘要。我们考虑了一类希尔伯特空间中的凸优化问题，这些问题可以通过执行一次投影求解，即把一个不可行点投影到可行集上。通过考虑以下问题，我们的结果改进了 Nurminski（2015）在线性规划设置中建立的结果：(i) 可能有多个解；(ii) 不满足严格的互补条件；(iii) 具有非线性凸约束。作为分析的副产品，我们对不可行点与可行集之间的必要距离进行了定量估计，以使其投影成为问题的解。我们的分析依赖于约束集的 "锐度 "属性，这是我们在此引入的一个新属性。

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Single-Projection Procedure for Infinite Dimensional Convex Optimization Problems

SIAM Journal on Optimization, Volume 34, Issue 2, Page 1646-1678, June 2024.
Abstract. We consider a class of convex optimization problems in a Hilbert space that can be solved by performing a single projection, i.e., by projecting an infeasible point onto the feasible set. Our results improve those established for the linear programming setting in Nurminski (2015) by considering problems that (i) may have multiple solutions, (ii) do not satisfy strict complementarity conditions, and (iii) possess nonlinear convex constraints. As a by-product of our analysis, we provide a quantitative estimate on the required distance between the infeasible point and the feasible set in order for its projection to be a solution of the problem. Our analysis relies on a “sharpness” property of the constraint set, a new property we introduce here.

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来源期刊

SIAM Journal on Optimization 数学-应用数学

CiteScore

5.30

自引率

9.70%

发文量

101

审稿时长

6-12 weeks

期刊介绍： The SIAM Journal on Optimization contains research articles on the theory and practice of optimization. The areas addressed include linear and quadratic programming, convex programming, nonlinear programming, complementarity problems, stochastic optimization, combinatorial optimization, integer programming, and convex, nonsmooth and variational analysis. Contributions may emphasize optimization theory, algorithms, software, computational practice, applications, or the links between these subjects.