Abstract

Convex non linear optimization problems may not have a solution in innite dimension spaces. The aim of this paper is to formulate some new results in this topic by using "technical regularization" of the objective function. The rst result shows that a non linear convex proper lower semi-continuous function, on a Banach space which have the Radon-Nikodym property, could be minimized by using a small regularization. while the second one shows that this regularization can be chosen as small as required. In addition, application tracks are presented and illustrated by elementary examples.