Dorina Jibetean

Semidefinite Approximations for Global Unconstrained Polynomial Optimization

  • Dorina Jibetean
  • Monique Laurent
    • Categories Global Optimization Theory, Semi-definite Programming, Unconstrained Optimization Tags ,

    We consider here the problem of minimizing a polynomial function on $\oR^n$. The problem is known to be hard even for degree $4$. Therefore approximation algorithms are of interest. Lasserre \cite{lasserre:2001} and Parrilo \cite{Pa02a} have proposed approximating the minimum of the original problem using a hierarchy of lower bounds obtained via semidefinite programming relaxations. We … Read more

    Global optimization of rational functions: a semidefinite programming approach

  • Etienne de Klerk
  • Dorina Jibetean
    • Categories Global Optimization Theory, Nonlinear Optimization, Semi-definite Programming Tags , , ,

    We consider the problem of global minimization of rational functions on $\LR^n$ (unconstrained case), and on an open, connected, semi-algebraic subset of $\LR^n$, or the (partial) closure of such a set (constrained case). We show that in the univariate case ($n=1$), these problems have exact reformulations as semidefinite programming (SDP) problems, by using reformulations introduced … Read more