Beyond Convex? Global Optimization is Feasible Only for Convex Objective Functions: A Theorem

Authors

R. Baker Kearfott
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

7-2004

Comments

Technical Report: UTEP-CS-03-28a

Published in Journal of Global Optimization, 2005, Vol. 33, No. 4, pp. 617-624.

Abstract

It is known that there are feasible algorithms for minimizing convex functions, and that for general functions, global minimization is a difficult (NP-hard) problem. It is reasonable to ask whether there exists a class of functions that is larger than the class of all convex functions for which we can still solve the corresponding minimization problems feasibly. In this paper, we prove, in essence, that no such more general class exists. In other words, we prove that global optimization is always feasible only for convex objective functions.