M. Rodríguez Álvarez
A set is evenly convex if it is the intersection of some family (possibly empty) of open halfspaces. This class of convex sets was introduced by Fenchel in 1952 in order to extend the polarity theory to nonclosed convex sets. In the eighties, Martínez-Legaz and Passy and Prisman, independently, started to use evenly convex sets in quasiconvex programming defining the evenly quasiconvex functions as those having evenly convex sublevel sets.
In this talk, we consider the class of evenly convex sets as an extension of the closed convex sets one and show that it captures the most outstanding properties of this subclass. Moreover, we define the so-called evenly convex functions as those functions whose epigraphs are evenly convex and study the main properties of this class of convex functions that contains the important class of lower semicontinuous convex functions.
Keywords: Linear systems, strict inequalities, even convexity, convex functions
Scheduled
GT11-5 MA-5 Continuous Optimization. Tribute to Marco Antonio López
September 6, 2019 12:40 PM
I2L7. Georgina Blanes building