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Relaxation methods for nonconvex quadratic programs

Paper Authors:

Benjamin Beach,

Robert Burlacu,

Andreas Barmann,

Lukas Hager,

Robert Hildebrand


Key Details

Presents novel MIP relaxations NMDT and D-NMDT for nonconvex MIQCQPs

D-NMDT enhances NMDT via double discretization for greater accuracy

D-NMDT uses fewer binaries than NMDT for same accuracy on dense problems

Numerical study shows D-NMDT computes much tighter bounds than NMDT

D-NMDT finds near-optimal solutions when combined with an NLP solver

AI generated summary

Relaxation methods for nonconvex quadratic programs

This paper introduces and analyzes new mixed-integer programming relaxation techniques for solving difficult nonconvex quadratic optimization problems. The methods approximate the nonlinear terms via piecewise linear functions. Computational experiments demonstrate the techniques can find high-quality solutions.

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