A correlative sparsity pattern graph is defined to find a certain sparse structure in the objective and constraint polynomials of a POP. Based on this graph, sets of supports for sums of squares (SOS) polynomials that lead to efficient SOS and semidefinite programming (SDP) relaxations are ...
In particular, we derive a short and direct proof for Lasserre's theorem on the existence of sums of squares certificates respecting the block structure. The motivation for the results can be found in the literature on numerical methods for global optimization of polynomials that exploit sparsity....
positive polynomialssum of squaressemidefinite programmingSEMIDEFINITE PROGRAMGLOBAL OPTIMIZATIONEXPLOITING SPARSITYSQUARESSUMSSETSWe consider a polynomial programming problem P on a compact basic semialgebraic set K subset of R-n, described by m polynomial inequalities g(j) (X) >= 0, and with criterion...