On the Complexity of Optimization Over the Standard Simplex

CentER Discussion Paper Series No. 2005-125

12 Pages Posted: 11 Jan 2006

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

E.G. Elabwabi

Tilburg University - Department of Econometrics & Operations Research

Date Written: December 6, 2005

Abstract

We review complexity results for minimizing polynomials over the standard simplex and unit hypercube.

In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing Lipschitz continuous functions and functions with uniformly bounded Hessians over the standard simplex.This extends an earlier result by De Klerk, Laurent and Parrilo [A PTAS for the minimization of polynomials of fixed degree over the simplex, Theoretical Computer Science, to appear.]

Keywords: global optimization, standard simplex, PTAS, multivariate Bernstein approximation, semidefinite programming

JEL Classification: C61

Suggested Citation

de Klerk, Etienne and den Hertog, Dick and Elabwabi, E.G., On the Complexity of Optimization Over the Standard Simplex (December 6, 2005). CentER Discussion Paper Series No. 2005-125. Available at SSRN: https://ssrn.com/abstract=874706 or http://dx.doi.org/10.2139/ssrn.874706

Etienne De Klerk (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

Dick Den Hertog

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

E.G. Elabwabi

Tilburg University - Department of Econometrics & Operations Research ( email )

Tilburg, 5000 LE
Netherlands

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