Maximal quasimonotonicity and dense single-directional properties of quasimonotone operators

• 成果类型: Article
• 署名作者: Aussel, D.; Eberhard, A.
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Universite Perpignan Via Domitia; Royal Melbourne Institute of Technology (RMIT)
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0658-8
• 发表日期: 2013
• 页码: 27-54
• 关键词: convex; sets

摘要

The concept of maximal quasimonotonicity of set-valued map is introduced and studied. Regularity properties of this class of operators is investigated, in particular the ccvc property, an adaptation to the quasimonotone case of the classical notion of cusco map. In an Asplund space, we provide sufficient conditions for a ccvc quasimonotone operator to be single-directional on a -dense subset.