A geometrical insight on pseudoconvexity and pseudomonotonicity

• 成果类型: Article; Proceedings Paper
• 署名作者: Crouzeix, Jean-Pierre; Eberhard, Andrew; Ralph, Daniel
• 署名单位: Universite Clermont Auvergne (UCA); Royal Melbourne Institute of Technology (RMIT); University of Cambridge
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-009-0324-3
• 发表日期: 2010
• 页码: 61-83
• 关键词: indirect utility-functions; quasi-convex; revealed preference; generalized monotonicity; Duality; differentiability; continuity

摘要

Generalised convexity is revisited from a geometric point of view. A substitute to the subdifferential is proposed. Then generalised monotonicity is considered. A representation of generalised monotone maps allows us to obtain a symmetry between maps and their inverses. Finally, maximality of generalised monotone maps is analysed.