First- and Second-Order Asymptotic Analysis with Applications in Quasiconvex Optimization

We use asymptotic analysis to describe in amore systematic way the behavior at the infinity of functions in the convex and quasiconvex case. Starting from the formulae for the firstand second-order asymptotic function in the convex case, we introduce similar notions suitable for dealing with quasiconvex functions. Afterward, by using such notions, a class of quasiconvex vector mappings under which the image of a closed convex set is closed, is introduced; we characterize the nonemptiness and boundedness of the set of minimizers of any lsc quasiconvex function; finally, we also characterize boundedness from below, along lines, of any proper and lsc function.