# Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization

@inproceedings{Parrilo2000StructuredSP, title={Structured semidefinite programs and semialgebraic geometry methods in robustness and optimization}, author={Pablo A. Parrilo}, year={2000} }

In the first part of this thesis, we introduce a specific class of Linear Matrix Inequalities (LMI) whose optimal solution can be characterized exactly. This family corresponds to the case where the associated linear operator maps the cone of positive semidefinite matrices onto itself. In this case, the optimal value equals the spectral radius of the operator. It is shown that some rank minimization problems, as well as generalizations of the structured singular value ($mu$) LMIs, have exactly…

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