General lagrange-type functions in constrained global optimization part II: Exact auxiliary functions

Abstract

This paper is a continuation of [13]. For each constrained optimization problem we consider certain unconstrained problems, which are constructed by means of auxiliary (Lagrange-type) functions. We study only exact auxiliary functions, it means that the set of their global minimizers coincides with the solution set of the primal constrained optimization problem. Sufficient conditions for the exactness of an auxiliary function are given. These conditions are obtained without assumption that the Lagrange function has a saddle point. Some examples of exact auxiliary functions are given.

Keywords:

• Constrained optimization
• Auxiliary function
• Exact auxiliary function
• Convolution function
• Generalized polar function