Gamal Elabwabi

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

  • Etienne de Klerk
  • Dick den Hertog
  • Gamal Elabwabi
    • Categories Global Optimization, Nonlinear Optimization, Semi-definite Programming Tags , ,

    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 … Read more

    On the complexity of optimization over the standard simplex

  • Etienne de Klerk
  • Dick den Hertog
  • Gamal Elabwabi
    • Categories Global Optimization Theory, Linear, Cone and Semidefinite Programming Tags , , , ,

    We review complexity results for minimizing polynomials over the standard simplex and unit hypercube. In addition, we show that there exists a polynomial time approximation scheme (PTAS) for minimizing some classes of functions (including Lipschitz continuous functions) over the standard simplex. The main tools used in the analysis are Bernstein approximation and Lagrange interpolation on … Read more