A Proximal Dynamic Approach to Equilibrium Problems With Finite-Time Convergence

• 成果类型: Article
• 署名作者: Ju, Xingxing; Li, Chuandong; He, Xing; Feng, Gang
• 署名单位: Southwest University - China; City University of Hong Kong
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3326713
• 发表日期: 2024
• 页码: 1773-1780
• 关键词: convergence; optimization; mathematical models; dynamical systems; Integrated circuit modeling; Heuristic algorithms; Robustness; Absolute value equations; Composite optimization; equilibrium problems; Finite-time convergence; proximal dynamics

摘要

This article proposes a finite-time converging proximal dynamic model (FPD) to deal with equilibrium problems. A distinctive feature of the FPD is its fast and finite-time convergence, in contrast to conventional proximal dynamic methods. It is shown that the solution of the proposed FPD converges to the solution of the corresponding equilibrium problems in finite-time under some mild conditions. Then the proposed FPD is applied to solve problems of nonsmooth composite optimization and absolute value equations. It is further shown in the case of solving composite optimization problems that the equilibrium point of the proposed proximal gradient dynamic model is globally finite-time stable under the so-called proximal Polyak-Lojasiewicz condition, which is weaker than strong convexity. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods.