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

Authors:
Vladik Kreinovich;R. Baker Kearfott
Affiliations:
Department of Computer Science, University of Texas at El Paso, El Paso 79968;Department of Mathematics, University of Louisiana, Lafayette 70504-1010
Venue:
Journal of Global Optimization
Year:
2005

Citing 1
Cited 5

Nonlinear optimization: complexity issues

Nonlinear optimization: complexity issues

Design and evaluation of multichannel multirate wireless networks

Mobile Networks and Applications
An adaptive contention-based scheduling scheme for proportional service differentiation in multichannel wireless networks

QShine '06 Proceedings of the 3rd international conference on Quality of service in heterogeneous wired/wireless networks
Using expert knowledge in solving the seismic inverse problem

International Journal of Approximate Reasoning
Computing optimal solutions of a linear programming problem with interval type-2 fuzzy constraints

HAIS'12 Proceedings of the 7th international conference on Hybrid Artificial Intelligent Systems - Volume Part I
A branch and bound algorithm for the global optimization of Hessian Lipschitz continuous functions

Journal of Global Optimization

Quantified Score

Hi-index	0.00

Visualization

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.