Optimization of Polynomial Functions

http://dx.doi.org/10.4153/CMB-2003-054-7
Canad. Math. Bull. 46(2003), 575-587

  Published:2003-12-01
 Printed: Dec 2003

This paper develops a refinement of Lasserre's algorithm for optimizing a polynomial on a basic closed semialgebraic set via semidefinite programming and addresses an open question concerning the duality gap. It is shown that, under certain natural stability assumptions, the problem of optimization on a basic closed set reduces to the compact case.