NECESSARY AND SUFFICIENT CONDITIONS FOR THE GLOBAL MINIMUM

Necessary and sufficient conditions for a local minimum form a well-developed chapter of optimization theory. Determinetion of such condi-tions for the global minimum is a challenging problem. Useful conditions are currently known only for a few classes of optimization problems including convex problems and some of their generalizations. It is important to find different classes of problems for which the required conditions can be obtained. In this paper, we examine one of these classes: the minimization of the problem over an arbitrary closed set U for a class of ordered normed spaces, where S is a bounded set. We use structure of the objective function in order to present necessary and sufficient conditions that give a clear undrestanding of the structure of a global minimizer and can be easily verified for some problems under consideration.

Keywords:

Simultaneous metric projection , downward and upwaed set , global minimum