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
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Indexed by:Journal Papers
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.
