Semidefinite Programming Relaxation vs Polyhedral Homotopy ...
Semidefinite Programming Relaxation vs Polyhedral Homotopy ...
Semidefinite Programming Relaxation vs Polyhedral Homotopy ...
You also want an ePaper? Increase the reach of your titles
YUMPU automatically turns print PDFs into web optimized ePapers that Google loves.
Katsura n system of polynomial equations; n = 8 case0 = −x 1 + 2x 2 9 + 2x 2 8 + 2x 2 7 + · · · + 2x 2 2 + x 2 1,0 = −x 2 + 2x 9 x 8 + 2x 8 x 7 + 2x 7 x 6 + · · · + 2x 3 x 2 + 2x 2 x 1 ,· · · · · · not c-sparse0 = −x 8 + 2x 9 x 2 + 2x 8 x 1 + 2x 7 x 2 + 2x 6 x 3 + 2x 5 x 4 ,1 = 2x 9 + 2x 8 + 2x 7 + 2x 6 + 2x 5 + 2x 4 + 2x 3 + 2x 2 + x 1 .Numerical results on SparsePOP (WKKM 2004)n obj.funct. relax. order r cpu∑8 xi ↑ 1 0.08∑8 x2i ↓ 2 7.1∑11 xi ↑ 1 0.14∑11 x2i ↓ 2 101.3Numerical results on HOM4PS (Li-Li-Gao 2002)n cpu sec. #solutions8 1.9 25611 209.1 2048Workshop on Advances in Optimization, April 19-21, 2007 – p.14/24