Journal of Global Optimization

, Volume 33, Issue 4, pp 617–624

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

Article

DOI: 10.1007/s10898-004-2120-1

Cite this article as:
Kreinovich, V. & Kearfott, R.B. J Glob Optim (2005) 33: 617. doi:10.1007/s10898-004-2120-1

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.

Keywords

Computational complexityGlobal optimizationNon-convexity

Copyright information

© Springer 2005

Authors and Affiliations

  1. 1.Department of Computer ScienceUniversity of Texas at El PasoEl Paso
  2. 2.Department of MathematicsUniversity of LouisianaLafayette