Approximation of quasiconvex functions by neatly quasiconvex functions

Abstract

A local minimum of a quasiconvex function is not necessarily a global minimum. In this paper, we show that every lower semicontinuous quasiconvex function can be approximated uniformly by a sequence of quasiconvex functions for which every local minimum is a global minimum. We also study the continuity of the functions appearing in a recently obtained decomposition of quasiconvex functions.