On approximate starshapedness in multiobjective optimization. (3rd March 2016)

• Record Type: Journal Article
• Authors: Al-Shamary, Bader; Mishra, S.K.; Laha, Vivek
• Is Part Of: Optimization methods and software. Volume 31:Number 2(2016)
• Page Start: 290
• Page End: 304
• Publication Date: 2016-03-03
• Subjects: multiobjective optimization problems -- approximate starshapedness -- Fréchet subdifferentials -- vector variational inequalities -- approximate efficiency -- equi-subdifferentiability; 90C26 -- 90C29 -- 90C30 -- 49J40 -- 49J50 -- 49J52; Mathematical optimization -- Periodicals; Algorithms -- Periodicals; 519.7
• DOI: 10.1080/10556788.2015.1064917
• Languages: English
• ISSNs: 1055-6788

Abstract

Abstract : In this paper, we give the vector versions of the concepts of approximate starshapedness, equi-subdifferentiability and pseudo-equi-subdifferentiability and establish relationships among approximate vector starshapedness, vector-equi-subdifferentiability and vector-pseudo-equi-subdifferentiability. We extend the concept of ε -quasi-efficient solutions in the context of multiobjective optimization problems involving approximately starshaped functions and use approximate vector variational inequalities of Stampacchia and Minty type in terms of Fréchet subdifferentials to characterize approximate efficient solutions.