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
Date Written: April 11, 2006
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: Suggested Citation