Exact and approximate vector Ekeland variational principles. (9th December 2022)

• Record Type: Journal Article
• Authors: Bao, T. Q.; Gutiérrez, C.; Novo, V.; Ródenas-Pedregosa, J. L.
• Is Part Of: Optimization. Volume 71:Number 15(2022)
• Page Start: 4497
• Page End: 4527
• Publication Date: 2022-12-09
• Subjects: Ekeland variational principle -- Dancs–Hegedüs–Medvegyev's fixed point theorem -- vector optimization -- scalarization -- strictly decreasing cone lower semicontinuity; 47H10 -- 49J53 -- 90C29; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.1949315
• Languages: English
• ISSNs: 0233-1934

Abstract

Abstract : This paper concerns with exact and approximate Ekeland variational principles for vector-valued functions and bifunctions that are derived via linear and nonlinear scalarization processes by an approximate scalar formulation of the Ekeland variational principle and a revised version of Dancs–Hegedüs–Medvegyev's fixed point theorem. Both results are also interesting in themselves and involve really mild assumptions. As a result, the obtained Ekeland variational principles improve some recent results in the literature since weaker assumptions are required.