具有非凸非光滑项的非凸线性最小问题的近似近似梯度算法

IF 1.8 3区数学 Q1 Mathematics

Journal of Global Optimization Pub Date : 2024-03-25 DOI:10.1007/s10898-024-01383-3

Jiefei He, Huiling Zhang, Zi Xu

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引用次数: 0

摘要

非凸最小问题在机器学习、无线通信和许多其他领域引起了极大关注。本文提出了一种高效的近似梯度算法，用于求解一类带有非凸非光滑项的非凸线性 minimax 问题，且找到 \(\varepsilon \)-驻点的迭代次数上界为\({\mathcal {O}}(\varepsilon ^{-3})\)。在大规模 MIMO 系统中的单比特预编码问题和分布式非凸优化问题上的一些数值结果证明了所提算法的有效性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms

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An approximation proximal gradient algorithm for nonconvex-linear minimax problems with nonconvex nonsmooth terms

Nonconvex minimax problems have attracted significant attention in machine learning, wireless communication and many other fields. In this paper, we propose an efficient approximation proximal gradient algorithm for solving a class of nonsmooth nonconvex-linear minimax problems with a nonconvex nonsmooth term, and the number of iteration to find an \(\varepsilon \)-stationary point is upper bounded by \({\mathcal {O}}(\varepsilon ^{-3})\). Some numerical results on one-bit precoding problem in massive MIMO system and a distributed non-convex optimization problem demonstrate the effectiveness of the proposed algorithm.

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来源期刊

Journal of Global Optimization 数学-应用数学

CiteScore

0.10

自引率

5.60%

发文量

137

审稿时长

6 months

期刊介绍： The Journal of Global Optimization publishes carefully refereed papers that encompass theoretical, computational, and applied aspects of global optimization. While the focus is on original research contributions dealing with the search for global optima of non-convex, multi-extremal problems, the journal’s scope covers optimization in the widest sense, including nonlinear, mixed integer, combinatorial, stochastic, robust, multi-objective optimization, computational geometry, and equilibrium problems. Relevant works on data-driven methods and optimization-based data mining are of special interest. In addition to papers covering theory and algorithms of global optimization, the journal publishes significant papers on numerical experiments, new testbeds, and applications in engineering, management, and the sciences. Applications of particular interest include healthcare, computational biochemistry, energy systems, telecommunications, and finance. Apart from full-length articles, the journal features short communications on both open and solved global optimization problems. It also offers reviews of relevant books and publishes special issues.