Improved convergence analysis of a smoothing Newton method for the circular cone programming. (3rd July 2022)

• Record Type: Journal Article
• Authors: Tang, Jingyong; Zhou, Jinchuan
• Is Part Of: Optimization. Volume 71:Number 7(2022)
• Page Start: 2005
• Page End: 2031
• Publication Date: 2022-07-03
• Subjects: Circular cone programming -- smoothing Newton method -- derivative-free line search -- quadratical convergence; 90C05 -- 90C22 -- 90C25 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1847108
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: In this paper, we propose a new smoothing Newton method to solve the circular cone programming (denoted by CCP). The proposed method is designed based on a non-monotone derivative-free line search scheme. We show that any accumulation point of the iteration sequence generated by this method is a solution of the CCP. Moreover, we prove that the proposed method is locally quadratically convergent without requiring strict complementarity conditions. Compared with existing smoothing Newton methods for solving the CCP, our method has three new features: (i) the generated iteration sequence is bounded; (ii) the value of the merit function converges to zero; (iii) the whole iteration sequence converges to an accumulation point if this point is isolated. Some numerical results are reported.