Software
There are many good software codes for semidefinite programming. Among the most well-known, the following ones are presented:
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SeDuMi, originally by Jos Sturm, now being maintained by the optimization group at McMaster University
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SDPT3, by Kim-Chuan Toh, Reha Tütüncü, and Mike Todd
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SDPA, by the research group of Masakazu Kojima
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A very convenient way of using these (and other) SDP solvers under MATLAB® is through the YALMIP Parser/Solver by Johan Löfberg.