On Lipschitz continuity of approximate solutions to set-valued equilibrium problems via nonlinear scalarization. (1st February 2023)

• Record Type: Journal Article
• Authors: Anh, Lam Quoc; Tam, Tran Ngoc; Danh, Nguyen Huu
• Is Part Of: Optimization. Volume 72:Number 2(2023)
• Page Start: 439
• Page End: 461
• Publication Date: 2023-02-01
• Subjects: Lipschitz continuity -- approximate solution -- equilibrium problem -- Browder variational inclusion -- nonlinear scalarization; 49K40 -- 90C31 -- 91B50; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1970753
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : In this paper, we consider parametric set-valued equilibrium problems in normed spaces. By virtue of the Gerstewitz nonlinear scalarization function along with relaxed concavity assumptions, we obtain the Lipschitz continuity property of solution maps to such problems. The treatment and obtained results for these problems are new and different from the existing ones in the literature. We apply the main results to the Browder variational inclusion to illustrate for their applicability.