This is a package for solving semidefinite programming (SDP) problems.
Given symmetric matrices $C, A_i$ and a vector $b$, the primal SDP problem is
$$min_{X} \, C \bullet X \,\,\, s.t. \,\,\, A_i \bullet X = b_i \, and \, X \geq 0$$
and the dual SDP problem is
$$max_{y,Z} \, \sum_i b_i y_i \,\,\, s.t. \,\,\, Z = C - \sum_i y_i A_i \, and \, Z \geq 0$$
We can construct a semidefinite program using the method sdp.
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The semidefinite program can be solved numerically using the method optimize.
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See Solver for a discussion of the available SDP solvers. The method refine can be used to improve the precision of the solution.
In small cases it is possible to solve the SDP symbolically, by forming the ideal of critical equations.
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This documentation describes version 0.3 of SemidefiniteProgramming.
If you have used this package in your research, please cite it as follows:
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The object SemidefiniteProgramming is a package, defined in SemidefiniteProgramming.m2, with auxiliary files in SemidefiniteProgramming/.
The source of this document is in SemidefiniteProgramming/SDPdoc.m2:39:0.