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On Indefinite Quadratic Optimization over the Intersection of Balls and Linear Constraints

Author

Listed:
  • Temadher A. Almaadeed

    (Qatar University)

  • Saeid Ansary Karbasy

    (University of Guilan)

  • Maziar Salahi

    (University of Guilan)

  • Abdelouahed Hamdi

    (Qatar University)

Abstract

In this paper, we study the minimization of an indefinite quadratic function over the intersection of balls and linear inequality constraints (QOBL). Using the hyperplanes induced by the intersection of each pair of balls, we show that the optimal solution of QOBL can be found by solving several extended trust-region subproblems (e-TRS). To solve e-TRS, we use the alternating direction method of multipliers approach and a branch and bound algorithm. Numerical experiments show the efficiency of the proposed approach compared to the CVX and the extended adaptive ellipsoid-based algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:194:y:2022:i:1:d:10.1007_s10957-022-02018-x
    DOI: 10.1007/s10957-022-02018-x
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    References listed on IDEAS

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    1. Lijun Xu & Bo Yu & Yin Zhang, 2017. "An alternating direction and projection algorithm for structure-enforced matrix factorization," Computational Optimization and Applications, Springer, vol. 68(2), pages 333-362, November.
    2. Maziar Salahi & Akram Taati & Henry Wolkowicz, 2017. "Local nonglobal minima for solving large-scale extended trust-region subproblems," Computational Optimization and Applications, Springer, vol. 66(2), pages 223-244, March.
    3. Mohammad Keyanpour & Naser Osmanpour, 2018. "On solving quadratically constrained quadratic programming problem with one non-convex constraint," OPSEARCH, Springer;Operational Research Society of India, vol. 55(2), pages 320-336, June.
    4. X. Zheng & X. Sun & D. Li, 2011. "Nonconvex quadratically constrained quadratic programming: best D.C. decompositions and their SDP representations," Journal of Global Optimization, Springer, vol. 50(4), pages 695-712, August.
    5. Davood Hajinezhad & Qingjiang Shi, 2018. "Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications," Journal of Global Optimization, Springer, vol. 70(1), pages 261-288, January.
    6. NESTEROV, Yu. & WOLKOWICZ, Henry & YE, Yinyu, 2000. "Semidefinite programming relaxations of nonconvex quadratic optimization," LIDAM Reprints CORE 1471, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. 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.
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