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A branch and bound algorithm for nonconvex quadratic optimization with ball and linear constraints

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  • Amir Beck

    (Technion - Israel Institute of Technology)

  • Dror Pan

    (Technion - Israel Institute of Technology)

Abstract

We suggest a branch and bound algorithm for solving continuous optimization problems where a (generally nonconvex) objective function is to be minimized under nonconvex inequality constraints which satisfy some specific solvability assumptions. The assumptions hold for some special cases of nonconvex quadratic optimization problems. We show how the algorithm can be applied to the problem of minimizing a nonconvex quadratic function under ball, out-of-ball and linear constraints. The main tool we utilize is the ability to solve in polynomial computation time the minimization of a general quadratic under one Euclidean sphere constraint, namely the so-called trust region subproblem, including the computation of all local minimizers of that problem. Application of the algorithm on sparse source localization problems is presented.

Suggested Citation

  • Amir Beck & Dror Pan, 2017. "A branch and bound algorithm for nonconvex quadratic optimization with ball and linear constraints," Journal of Global Optimization, Springer, vol. 69(2), pages 309-342, October.
    • Handle: RePEc:spr:jglopt:v:69:y:2017:i:2:d:10.1007_s10898-017-0521-1
    DOI: 10.1007/s10898-017-0521-1
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    References listed on IDEAS

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    1. Jos F. Sturm & Shuzhong Zhang, 2003. "On Cones of Nonnegative Quadratic Functions," Mathematics of Operations Research, INFORMS, vol. 28(2), pages 246-267, May.
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    Cited by:

    1. Nadav Hallak & Marc Teboulle, 2020. "Finding Second-Order Stationary Points in Constrained Minimization: A Feasible Direction Approach," Journal of Optimization Theory and Applications, Springer, vol. 186(2), pages 480-503, August.
    2. Temadher A. Almaadeed & Saeid Ansary Karbasy & Maziar Salahi & Abdelouahed Hamdi, 2022. "On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints," Journal of Optimization Theory and Applications, Springer, vol. 194(1), pages 246-264, July.
    3. Saeid Ansary Karbasy & Maziar Salahi, 2022. "On the branch and bound algorithm for the extended trust-region subproblem," Journal of Global Optimization, Springer, vol. 83(2), pages 221-233, June.
    4. M. Locatelli, 2023. "KKT-based primal-dual exactness conditions for the Shor relaxation," Journal of Global Optimization, Springer, vol. 86(2), pages 285-301, June.

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