Optimization of Univariate Functions on Bounded Intervals by Interpolation and Semidefinite Programming

CentER Discussion Paper Series No. 2006-26

21 Pages Posted: 9 May 2006

See all articles by Etienne de Klerk

Etienne de Klerk

Tilburg University

E.G. Elabwabi

Tilburg University - Department of Econometrics & Operations Research

Dick den Hertog

Tilburg University - Department of Econometrics & Operations Research

Date Written: April 11, 2006

Abstract

We consider the problem of minimizing a univariate function f on an interval [a, b]. When f is a polynomial, we review how this problem may be reformulated as a semidefinite programming (SDP) problem, and review how to extract all global minimizers from the solution of the SDP problem. For general f, we approximate the global minimum by minimizing the Lagrange or Hermite interpolant of f on the Chebyshev nodes using the SDP approach. We provide numerical results for a set of test functions.

JEL Classification: C61

Suggested Citation

de Klerk, Etienne and Elabwabi, E.G. and den Hertog, Dick, Optimization of Univariate Functions on Bounded Intervals by Interpolation and Semidefinite Programming (April 11, 2006). CentER Discussion Paper Series No. 2006-26. Available at SSRN: https://ssrn.com/abstract=900108 or http://dx.doi.org/10.2139/ssrn.900108

Etienne De Klerk (Contact Author)

Tilburg University ( email )

P.O. Box 90153
Tilburg, 5000 LE
Netherlands

E.G. Elabwabi

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

Tilburg, 5000 LE
Netherlands

Dick Den Hertog

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

Tilburg, 5000 LE
Netherlands

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