Optimization of univariate functions on bounded intervals by interpolation and semidefinite programming
Etienne De Klerk (E.deKlerkuvt.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.
Entry Submitted: 04/24/2006
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