GENERIC EXISTENCE OF SOLUTIONS OF MINIMIZATION PROBLEMS WITH AN INCREASING COST FUNCTION

Abstract

In this work we consider the minimization problem f(x)-> min, x in K, K is a closed subset of an ordered Banach space X and f belongs to a space of increasing lower semicontinuous functions on K We show that for most functions f in this space the corresponding minimization problem has a unique solution This result is an extension of a related result in to a larger class of functions