吴佳

Professor   Supervisor of Doctorate Candidates   Supervisor of Master's Candidates

Gender:Female

Alma Mater:大连理工大学

Degree:Doctoral Degree

School/Department:数学科学学院

Discipline:Operation Research and Control Theory

Business Address:创新园大厦B1207

E-Mail:wujia@dlut.edu.cn


Paper Publications

The rate of convergence of proximal method of multipliers for equality constrained optimization problems

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Indexed by:Journal Papers

First Author:Zhang, Yule

Correspondence Author:Zhang, LW (corresponding author), Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China.

Co-author:Wu, Jia,Zhang, Liwei

Date of Publication:2020-09-01

Journal:OPTIMIZATION LETTERS

Included Journals:SCIE

Volume:14

Issue:6

Page Number:1599-1613

ISSN No.:1862-4472

Key Words:Equality constrained optimization; Rate of convergence; The proximal method of multipliers

Abstract:The proximal method of multipliers was proposed by Rockafellar (Math Oper Res 1:97-116, 1976) for solving convex programming and it is a kind of proximal point method for convex programming. In this paper, we apply this method for equality constrained optimization problems, in which subproblems have better properties than those from the augmented Lagrange method. We prove that, under linear independence constraint qualification and the second-order sufficiency optimality condition, the rate of convergence of the proximal method of multipliers, for the equality constrained optimization problem, is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold c(*) > 0. Moreover, the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to +infinity.

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