Fernando Flores-Bazán, Fabián Flores-Bazán, Cristian Vera:
Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives
This paper deals with maximization and minimization of quasiconvex functions in a finite dimensional setting. Firstly, some existence results on closed convex sets, possibly containing lines, are presented. Necessary or sufficient optimality conditions are derived in terms of radial epiderivatives. Finally, some attempts to define asymptotic functions under quasiconvexity are also outlined. Several examples illustrating the applicability of our results are shown.
This preprint gave rise to the following definitive publication(s):
Fernando FLORES-BAZáN, Fabián FLORES-BAZáN, Cristian VERA: Maximizing and minimizing quasiconvex functions: related properties, existence and optimality conditions via radial epiderivatives. Journal of Global Optimization, vol. 63, 1, pp. 99-123, (2015).