Quasiconvex optimization problems and asymptotic analysis in Banach spaces. (1st November 2020)

• Record Type: Journal Article
• Authors: Iusem, A.; Lara, F.
• Is Part Of: Optimization. Volume 69:Number 11(2020)
• Page Start: 2453
• Page End: 2470
• Publication Date: 2020-11-01
• Subjects: Asymptotic cones -- asymptotic functions -- quasiconvexity -- nonconvex optimization -- equilibrium problems; 90C26 -- 90C30; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1612893
• Languages: English
• ISSNs: 0233-1934

Abstract

ABSTRACT: We use asymptotic analysis for dealing with quasiconvex optimization problems in reflexive Banach spaces. We study generalized asymptotic (recession) cones for nonconvex and nonclosed sets and its respective generalized asymptotic functions. We prove that the generalized asymptotic functions defined in previous works directly through closed formulae can also be generated from the generalized asymptotic cones. We establish three characterizations results for the nonemptiness and compactness of the solution set for noncoercive quasiconvex minimization problems using different asymptotic functions. Finally, we present a sufficient condition for the nonemptiness and boundedness of the solution set for quasiconvex pseudomonotone equilibrium problems.