SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs

@article{Nohra2021SDPqualityBV,
  title={SDP-quality bounds via convex quadratic relaxations for global optimization of mixed-integer quadratic programs},
  author={Carlos J. Nohra and Arvind U. Raghunathan and Nikolaos V. Sahinidis},
  journal={Mathematical Programming},
  year={2021}
}
We consider the global optimization of nonconvex mixed-integer quadratic programs with linear equality constraints. In particular, we present a new class of convex quadratic relaxations which are derived via quadratic cuts. To construct these quadratic cuts, we solve a separation problem involving a linear matrix inequality with a special structure that allows the use of specialized solution algorithms. Our quadratic cuts are nonconvex, but define a convex feasible set when intersected with the… 
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  • Computer Science
    2021 60th IEEE Conference on Decision and Control (CDC)
  • 2021
TLDR
A novel Homogeneous QP (HQP) formulation which is obtained by embedding the original QP in a larger space and presenting an Infeasible Interior Point Method (IIPM) for the HQP and showing polynomial iteration complexity when applied to HQP.

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