TR2020-178

Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs


    •  Nohra, C.J., Raghunathan, A., Sahinidis, N.V., "Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs", SIAM Journal on Optimization, DOI: 10.1137/​19M1271762, Vol. 31, No. 1, pp. 142–171, December 2020.
      BibTeX TR2020-178 PDF
      • @article{Nohra2020dec2,
      • author = {Nohra, Carlos J. and Raghunathan, Arvind and Sahinidis, Nikolaos V.},
      • title = {Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs},
      • journal = {SIAM Journal on Optimization},
      • year = 2020,
      • volume = 31,
      • number = 1,
      • pages = {142–171},
      • month = dec,
      • doi = {10.1137/19M1271762},
      • url = {https://www.merl.com/publications/TR2020-178}
      • }
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  • Research Area:

    Optimization

Abstract:

We consider the global optimization of nonconvex quadratic programs and mixedinteger quadratic programs. We present a family of convex quadratic relaxations which are derived by convexifying nonconvex quadratic functions through perturbations of the quadratic matrix. We investigate the theoretical properties of these quadratic relaxations and show that they are equivalent to some particular semidefinite programs. We also introduce novel branching variable selection strategies which can be used in conjunction with the quadratic relaxations investigated in this paper. We integrate the proposed relaxation and branching techniques into the global optimization solver BARON, and test our implementation by conducting numerical experiments on a large collection of problems. Results demonstrate that the proposed implementation leads to very significant reductions in BARON’s computational times to solve the test problems

 

  • Related Publication

  •  Nohra, C.J., Raghunathan, A., Sahinidis, N.V., "Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs", arXiv, DOI: arXiv:2010.04822, pp. 1-33, June 2020.
    BibTeX arXiv
    • @article{Nohra2020jun,
    • author = {Nohra, Carlos J. and Raghunathan, Arvind and Sahinidis, Nikolaos V.},
    • title = {Spectral relaxations and branching strategies for global optimization of mixed-integer quadratic programs},
    • journal = {arXiv},
    • year = 2020,
    • pages = {1--33},
    • month = jun,
    • doi = {arXiv:2010.04822},
    • url = {https://arxiv.org/abs/2010.04822}
    • }