Semidefinite Programming Relaxation vs Polyhedral Homotopy ...

cyclic n system of polynomial equations: n = 5 case0 = x 1 + x 2 + x 3 + x 4 + x 5 ,0 = x 1 x 2 + x 2 x 3 + x 3 x 4 + x 4 x 5 + x 5 x 1 , not c-sparse0 = x 1 x 2 x 3 + x 2 x 3 x 4 + x 3 x 4 x 5 + x 4 x 5 x 1 + x 5 x 1 x 2 ,0 = x 1 x 2 x 3 x 4 + x 2 x 3 x 4 x 5 + x 3 x 4 x 5 x 1 + x 4 x 5 x 1 x 2 + x 5 x 1 x 2 x 3 ,0 = −1 + x 1 x 2 x 3 x 4 x 5 .Numerical results on SparsePOP: obj.funct.+lbd, ubd on x in obj.funct. relax. order r cpu5 ∑ x i ↑ 3 1.836 ∑ x i ↑ 4 753.2Numerical results on HOM4PS (Li-Li-Gao)n cpu sec.#solutions5 0.1 706 0.2 156Workshop on Advances in Optimization, April 19-21, 2007 – p.15/24