In this paper‎, ‎we introduce and study some new single-valued gap functions for non-differentiable semi-infinite multiobjective optimization problems with locally Lipschitz data‎. ‎Since one of the fundamental properties of gap function for optimization problems is its abilities in characterizing the solutions of the problem in question‎, ‎then the essential properties of the newly introduced ...

Suppose (ftj)ist.jtr is a pxp matrix of real-valued infinitely (respectively /«-times continuously) differentiable functions on an open subset fl of R". Then (fti)isi,isp maps the space of ^-tuples of distributions on fl (respectively distributions of order Smonfi) into itself. In the present paper, the pxp matrices (P/)isi,<sp for which this mapping is onto are characterized in terms of the ze...

Abstract. We prove that for every function f : X → Y , where X is a separable Banach space and Y is a Banach space with RNP, there exists a set A ∈ Ã such that f is Gâteaux differentiable at all x ∈ S(f) \ A, where S(f) is the set of points where f is pointwise-Lipschitz. This improves a result of Bongiorno. As a corollary, we obtain that every K-monotone function on a separable Banach space is...