Robust approximate optimal solutions for nonlinear semi-infinite programming with uncertainty. (1st September 2020)

• Record Type: Journal Article
• Authors: Sun, Xiangkai; Teo, Kok Lay; Zeng, Jing; Liu, Liying
• Is Part Of: Optimization. Volume 69:Number 9(2020)
• Page Start: 2109
• Page End: 2129
• Publication Date: 2020-09-01
• Subjects: Semi-infinite programming -- optimality conditions -- approximate duality -- saddle point theorem; 90C34 -- 90C26 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1763990
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we deal with robust approximate quasi optimal solutions for a class of nonlinear semi-infinite programming with data uncertainty (USIP) in both the objective and constraints. By using a new robust-type subdifferential constraint qualification and some generalized convexity assumptions, we first establish approximate optimality conditions for robust approximate quasi optimal solutions of (USIP) . Then, we introduce a Mixed-type robust approximate dual problem for (USIP) and investigate robust approximate duality relations between them. Furthermore, we establish a nonsmooth robust approximate saddle point theorem for an uncertain approximate Lagrangian function associated with (USIP) .