Optimization of univariate functions on bounded intervals by interpolation and semidefinite programming
نویسندگان
چکیده
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. AMS subject classification: 65D05, 65K05, 90C22
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