The rate of convergence of proximal method of multipliers for nonlinear programming. (2nd September 2020)

• Record Type: Journal Article
• Authors: Zhang, Yule; Wu, Jia; Zhang, Liwei
• Is Part Of: Optimization methods and software. Volume 35:Number 5(2020)
• Page Start: 1022
• Page End: 1049
• Publication Date: 2020-09-02
• Subjects: Nonlinear programming -- rate of convergence -- proximal method of multipliers -- strict complementarity; 90C30; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2020.1738435
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : We analyze the rate of convergence of the proximal method of multipliers for non-convex nonlinear programming problems. First, we prove, under the strict complementarity condition, that the rate of convergence of the proximal method of multipliers is linear and the ratio constant is proportional to 1/ c when the ratio ‖ ( μ 0, λ 0 ) − ( μ ¯, λ ¯ ) ‖ / c is small enough, which implies that the rate of convergence of the proximal method of multipliers is superlinear when the parameter c increases to + ∞ . Second, we prove that, without strict complementarity condition, the rate of convergence of the proximal method of multipliers is proportional to 1/ c when c exceeds a threshold.