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Penalized semidefinite programming for quadratically-constrained quadratic optimization

Author

Listed:
  • Ramtin Madani

    (University of Texas)

  • Mohsen Kheirandishfard

    (University of Texas)

  • Javad Lavaei

    (University of California)

  • Alper Atamtürk

    (University of California)

Abstract

In this paper, we give a new penalized semidefinite programming approach for non-convex quadratically-constrained quadratic programs (QCQPs). We incorporate penalty terms into the objective of convex relaxations in order to retrieve feasible and near-optimal solutions for non-convex QCQPs. We introduce a generalized linear independence constraint qualification (GLICQ) criterion and prove that any GLICQ regular point that is sufficiently close to the feasible set can be used to construct an appropriate penalty term and recover a feasible solution. Inspired by these results, we develop a heuristic sequential procedure that preserves feasibility and aims to improve the objective value at each iteration. Numerical experiments on large-scale system identification problems as well as benchmark instances from the library of quadratic programming demonstrate the ability of the proposed penalized semidefinite programs in finding near-optimal solutions for non-convex QCQP.

Suggested Citation

  • Ramtin Madani & Mohsen Kheirandishfard & Javad Lavaei & Alper Atamtürk, 2020. "Penalized semidefinite programming for quadratically-constrained quadratic optimization," Journal of Global Optimization, Springer, vol. 78(3), pages 423-451, November.
    • Handle: RePEc:spr:jglopt:v:78:y:2020:i:3:d:10.1007_s10898-020-00918-8
    DOI: 10.1007/s10898-020-00918-8
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    References listed on IDEAS

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    1. NESTEROV, Yu., 1998. "Semidefinite relaxation and nonconvex quadratic optimization," LIDAM Reprints CORE 1362, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
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