Characterizations of Approximate Duality and Saddle Point Theorems for Nonsmooth Robust Vector Optimization. (11th March 2020)

• Record Type: Journal Article
• Authors: Sun, Xiangkai; Tang, Liping; Zeng, Jing
• Is Part Of: Numerical functional analysis and optimization. Volume 41:Number 4(2020)
• Page Start: 462
• Page End: 482
• Publication Date: 2020-03-11
• Subjects: Approximate quasi solutions -- quasi saddle points -- robust vector optimization problems; 90C26 -- 90C29 -- 90C46; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2019.1660891
• Languages: English
• ISSNs: 0163-0563

Abstract

Abstract: This article deals with robust approximate Pareto efficient solutions for a class of nonsmooth vector optimization problems with data uncertainty. By using robust optimization and scalarization methodology, we first obtain some nonsmooth approximate optimality conditions for this uncertain optimization problem. Then, we introduce a Wolfe-type robust approximate dual problem for this uncertain optimization problem and obtain some nonsmooth robust approximate duality properties. Moreover, we investigate nonsmooth approximate saddle point theorems of an uncertain approximate vector Lagrangian function associated with this uncertain optimization problem.