SDPTools: High Precision SDP Solver in Maple
Feng Guo
TL;DR
SDPTools is a Maple package that enables high-precision semidefinite programming solutions, improving accuracy for applications like global optimization of rational functions where numerical errors are critical.
Contribution
The paper introduces SDPTools, a high-precision SDP solver in Maple, addressing numerical accuracy issues in fixed-precision solvers like Matlab-based ones.
Findings
Achieved the best numerical results for the Rumps Model Problem.
Demonstrated improved certification of global optima for rational functions.
Showcased high-precision capabilities in semidefinite programming.
Abstract
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.
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Taxonomy
TopicsAdvanced Optimization Algorithms Research · Computational Geometry and Mesh Generation · Robotic Path Planning Algorithms