Kim, H. Waki, Sparsity in sums of squares of polynomials, Mathematical Programming 103 (2005) 45-62.M. Kojima, S. Kim, and H. Waki, Sparsity in sums of squares of polynomials, Math. Program., 103 (2005), pp. 45-
Kim and H. Waki, "Sparsity in sums of squares of polynomials", Research Report B-391, Dept. of Mathematical and computing Sciences, Tokyo Institute of Technology, Meguro, Tokyo 152-8552, June 2003. Revised August 2003.Masakazu Kojima,Sunyong Kim,and Hayato Waki.Sparsity in sums of squares ...
This work derives upper bounds on the convergence rate of the moment-sum-of-squares hierarchy with correlative sparsity for global minimization of polynomials on compact basic semialgebraic sets. The main conclusion is that both sparse hierarchies based on the Schm眉dgen and Putinar Positivstellenst...
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...
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....