Semidefinite programming

3 Why Use SDP? 5 3.1 Tractable Relaxations of Max-Cut . . . . . . . . . . . . . . . . . . . . . . . . 5 3.1.1 Simple Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.2 Trust Region Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.3 Box Constraint Relaxation . . . . . . . . . . . . . . . . . . . . . . . . 6 3.1.4 Eigenvalue Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.5 SDP Bound . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 3.1.6 Summary and Lagrangian Relaxation . . . . . . . . . . . . . . . . . . 8 3.2 Recipe for SDP relaxations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 3.3 SDP Relaxation for the Quadratic Assignment Problem, QAP . . . . . . . . 9

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