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 nonlinear semidefinite programming

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Indexed by:Journal Papers

Date of Publication:2020-04-02

Journal:OPTIMIZATION

Volume:69

Issue:4

Page Number:875-900

ISSN No.:0233-1934

Key Words:Nonlinear semidefinite programming; rate of convergence; the proximal method of multipliers

Abstract:The proximal method of multipliers was proposed by Rockafellar [Augmented Lagrangians and applications of the proximal point algorithm in convex programming. Math Oper Res. 1976;1:97-116] for solving convex programming and it is a kind of proximal point method applied to convex programming. In this paper, we apply this method for solving nonlinear semidefinite programming problems, in which subproblems have better properties than those from the augmented Lagrange method. We prove that, under the linear independence constraint qualification and the strong second-order sufficiency optimality condition, the rate of convergence of the proximal method of multipliers, for a nonlinear semidefinite programming problem, is linear and the ratio constant is proportional to 1/c, where c is the penalty parameter that exceeds a threshold . Moreover, the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to .

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