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

Xingxing Ju; Chuandong Li; Xing He; Gang Feng

doi:10.1109/TAC.2023.3326713

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

Xingxing Ju, Chuandong Li^*, Xing He, Gang Feng

^*Corresponding author for this work

Department of Biomedical Engineering

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

12 Citations (Scopus)

Abstract

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. © 2023 IEEE.

Original language	English
Pages (from-to)	1773-1780
Journal	IEEE Transactions on Automatic Control
Volume	69
Issue number	3
Online published	23 Oct 2023
DOIs	https://doi.org/10.1109/TAC.2023.3326713
Publication status	Published - Mar 2024

Funding

This work was supported in part by the National Key Research and Development Project under Grant 2018AAA0100101, in part by the National Natural Science Foundation of China under Grant 62373310, Grant 61873213, Grant 62003281, and Grant 62176218, in part by the Fundamental Research Funds for the Central Universities under Grant XDJK2020TY003, Grant SWU020007, and Grant SWU020006, in part by the Graduate Student Innovation Project of Chongqing under Grant CYB21126, in part by the Sichuan Province Natural Science Foundation of China under Grant 2023NSFSC1433, in part by the Research Grants Council of Hong Kong under Grant CityU-11208223, and in part by the Natural Science Foundation of Chongqing under Grant cstc2021jcyj-msxmX1169.

Research Keywords

Absolute value equations
composite optimization
Convergence
Dynamical systems
equilibrium problems
finite-time convergence
Heuristic algorithms
Integrated circuit modeling
Mathematical models
Optimization
proximal dynamics
Robustness

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10.1109/TAC.2023.3326713

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@article{079a345f2d1e4a4fbb459b9cda7573c3,

title = "A Proximal Dynamic Approach to Equilibrium Problems With Finite-Time Convergence",

abstract = "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. {\textcopyright} 2023 IEEE.",

keywords = "Absolute value equations, composite optimization, Convergence, Dynamical systems, equilibrium problems, finite-time convergence, Heuristic algorithms, Integrated circuit modeling, Mathematical models, Optimization, proximal dynamics, Robustness",

author = "Xingxing Ju and Chuandong Li and Xing He and Gang Feng",

year = "2024",

month = mar,

doi = "10.1109/TAC.2023.3326713",

language = "English",

volume = "69",

pages = "1773--1780",

journal = "IEEE Transactions on Automatic Control",

issn = "0018-9286",

publisher = "IEEE",

number = "3",

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TY - JOUR

T1 - A Proximal Dynamic Approach to Equilibrium Problems With Finite-Time Convergence

AU - Ju, Xingxing

AU - Li, Chuandong

AU - He, Xing

AU - Feng, Gang

PY - 2024/3

Y1 - 2024/3

N2 - 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. © 2023 IEEE.

AB - 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. © 2023 IEEE.

KW - Absolute value equations

KW - composite optimization

KW - Convergence

KW - Dynamical systems

KW - equilibrium problems

KW - finite-time convergence

KW - Heuristic algorithms

KW - Integrated circuit modeling

KW - Mathematical models

KW - Optimization

KW - proximal dynamics

KW - Robustness

UR - http://www.scopus.com/inward/record.url?scp=85176378438&partnerID=8YFLogxK

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-85176378438&origin=recordpage

U2 - 10.1109/TAC.2023.3326713

DO - 10.1109/TAC.2023.3326713

M3 - RGC 21 - Publication in refereed journal

SN - 0018-9286

VL - 69

SP - 1773

EP - 1780

JO - IEEE Transactions on Automatic Control

JF - IEEE Transactions on Automatic Control

IS - 3

ER -

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

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GRF: Distributed Fixed-time Converging Nash Equilibrium Seeking for Non-cooperative Games over Multi-agent Networks and Applications

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

Abstract

Funding

Research Keywords

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GRF: Distributed Fixed-time Converging Nash Equilibrium Seeking for Non-cooperative Games over Multi-agent Networks and Applications

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