Levitin–Polyak well-posedness of generalized bilevel equilibrium problem with perturbations. (2nd November 2021)

• Record Type: Journal Article
• Authors: Virmani, Garima; Srivastava, Manjari
• Is Part Of: Optimization. Volume 70:Number 11(2021)
• Page Start: 2341
• Page End: 2355
• Publication Date: 2021-11-02
• Subjects: Generalized bilevel mixed equilibrium problem -- Levitin–Polyak well-posedness -- measure of non-compactness -- approximate solution set -- perturbations; 49J40 -- 90C33; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2020.1779720
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, a new class of problem known as the generalized bilevel mixed equilibrium problem with perturbations (GBMEPP) has been introduced on a real Banach space. Based on the diameter and the measure of non-compactness of the approximate solution set of the above stated problem, criteria and characterizations have been derived for Levitin–Polyak (LP) well-posedness. A sufficient condition for the LP well-posedness has also been derived assuming the boundedness of the approximate solution set.