polynomial optimization

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

    LMI approximations for cones of positive semidefinite forms

  • Javier F. Peña
  • Juan Vera
  • Luis F. Zuluaga
    • Categories Convex Optimization Tags , ,

    An interesting recent trend in optimization is the application of semidefinite programming techniques to new classes of optimization problems. In particular, this trend has been successful in showing that under suitable circumstances, polynomial optimization problems can be approximated via a sequence of semidefinite programs. Similar ideas apply to conic optimization over the cone of copositive … Read more