Characterizations of robust ε-quasi optimal solutions for nonsmooth optimization problems with uncertain data. (3rd April 2021)

• Record Type: Journal Article
• Authors: Sun, Xiang-Kai; Teo, Kok Lay; Long, Xian-Jun
• Is Part Of: Optimization. Volume 70:Number 4(2021)
• Page Start: 847
• Page End: 870
• Publication Date: 2021-04-03
• Subjects: Approximate solutions -- generalized subdifferential -- robust nonsmooth optimization; 90C26 -- 90C29 -- 90C46; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1871730
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: This paper deals with robust ε -quasi optimal solutions for a class of nonsmooth optimization problems with uncertain data. Under some mild assumptions, we first establish, by using robust optimization (i.e. worst-case) approach, approximate optimality conditions for this uncertain nonsmooth optimization problem. Then, we introduce a Mixed-type robust approximate dual problem of this uncertain optimization problem, and explore their relationships. Moreover, using a scalarization method, we derive optimality conditions for robust weakly approximate efficient solutions for an uncertain nonsmooth multiobjective optimization problem. We also obtain approximate duality theorems for the uncertain nonsmooth multiobjective optimization problem.