A stochastic approximation method for convex programming with many semidefinite constraints. (2nd January 2023)

• Record Type: Journal Article
• Authors: Li-Ping, Pang; Ming-Kun, Zhang; Xian-Tao, Xiao
• Is Part Of: Optimization methods and software. Volume 38:Number 1(2023)
• Page Start: 34
• Page End: 58
• Publication Date: 2023-01-02
• Subjects: Convex programming -- semidefinite programming with many constraints -- stochastic approximation -- convergence analysis -- error bound condition; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2022.2091563
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we consider a type of semidefinite programming problem (MSDP), which involves many (not necessarily finite) of semidefinite constraints. MSDP can be established in a wide range of applications, including covering ellipsoids problem and truss topology design. We propose a random method based on a stochastic approximation technique for solving MSDP, without calculating and storing the multiplier. Under mild conditions, we establish the almost sure convergence and expected convergence rates of the proposed method. A variety of simulation experiments are carried out to support our theoretical results.