Optimization of univariate functions on bounded intervals by interpolation and semidefinite programming

Etienne De Klerk (E.deKlerkuvt.nl)
Gamal Elabwabi (g.elabwabiewi.tudelft.nl)
Dick Den Hertog (D.denHertoguvt.nl)

Abstract: We consider the problem of minimizing a univariate, real-valued 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.

Keywords: line search, interpolation, semidefinite programming

Category 1: Global Optimization

Category 2: Linear, Cone and Semidefinite Programming (Semi-definite Programming )

Category 3: Nonlinear Optimization

Citation: CentER Discussion paper 2006-26, Tilburg University, The Netherlands, April 2006.

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Entry Submitted: 04/24/2006
Entry Accepted: 04/26/2006
Entry Last Modified: 04/27/2006

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