Two characterizations of quasiconvexity
W{\l}odzimierz Fechner
TL;DR
This paper introduces two new ways to characterize quasiconvex functions in real linear spaces, extending classical theorems and providing new insights into risk measures.
Contribution
It offers two novel characterizations of quasiconvexity for radially semicontinuous mappings and extends Sion's minimax theorem.
Findings
Extended Sion's minimax theorem
New characterization of quasiconvex risk measures
Two characterizations of quasiconvexity
Abstract
We present two characterizations of quasiconvexity for radially semicontinuous mappings defined on a convex subset of a real linear space. As an application we obtain an extension of the Sion's minimax theorem, as well as a new characterization of quasiconvex risk measures.
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Taxonomy
TopicsOptimization and Variational Analysis · Advanced Banach Space Theory · Analytic and geometric function theory