SDPTools: High Precision SDP Solver in Maple

Semidefinite programs are an important class of convex optimization problems. It can be solved efficiently by SDP solvers in Matlab, such as SeDuMi, SDPT3, DSDP. However, since we are running fixed precision SDP solvers in Matlab, for some applications, due to the numerical error, we can not get good results. SDPTools is a Maple package to solve SDP in high precision. We apply SDPTools to the certification of the global optimum of rational functions. For the Rumps Model Problem, we obtain the best numerical results so far. 1. Preliminaries SDPTools is a Maple package to solve a semidefinite program (SDP): minimize cx s.t. F (x ) ≥ 0 , (1) where F (x ) △ = F0 + m ∑