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Award ID contains: 1736326

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  1. ; (, Computational Optimization and Applications)
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  2. ; ; (, Journal of Optimization Theory and Applications)
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  3. ; ; ; (, Journal of Global Optimization)
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  4. ; ; (, IEEE Transactions on Power Systems)
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  5. ; ; (, Mathematical Programming Computation)
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  6. ; (, Computational Optimization and Applications)
    The problem of minimizing the rank of a symmetric positive semidefinite matrix subject to constraints can be cast equivalently as a semidefinite program with complementarity constraints (SDCMPCC). The formulation requires two positive semidefinite matrices to be complementary. This is a continuous and nonconvex reformulation of the rank minimization problem. We investigate calmness of locally optimal solutions to the SDCMPCC formulation and hence show that any locally optimal solution is a KKT point. We develop a penalty formulation of the problem. We present calmness results for locally optimal solutions to the penalty formulation. We also develop a proximal alternating linearized minimization (PALM) scheme for the penalty formulation, and investigate the incorporation of a momentum term into the algorithm. Computational results are presented. 
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