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A new algorithm for concave quadratic programming

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  • Moslem Zamani

    (Ton Duc Thang University
    Ton Duc Thang University)

Abstract

The main outcomes of the paper are divided into two parts. First, we present a new dual for quadratic programs, in which, the dual variables are affine functions, and we prove strong duality. Since the new dual is intractable, we consider a modified version by restricting the feasible set. This leads to a new bound for quadratic programs. We demonstrate that the dual of the bound is a semi-definite relaxation of quadratic programs. In addition, we probe the relationship between this bound and the well-known bounds in the literature. In the second part, thanks to the new bound, we propose a branch and cut algorithm for concave quadratic programs. We establish that the algorithm enjoys global convergence. The effectiveness of the method is illustrated for numerical problem instances.

Suggested Citation

  • Moslem Zamani, 2019. "A new algorithm for concave quadratic programming," Journal of Global Optimization, Springer, vol. 75(3), pages 655-681, November.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:3:d:10.1007_s10898-019-00787-w
    DOI: 10.1007/s10898-019-00787-w
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    References listed on IDEAS

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    Cited by:

    1. Moslem Zamani, 2023. "New bounds for nonconvex quadratically constrained quadratic programming," Journal of Global Optimization, Springer, vol. 85(3), pages 595-613, March.
    2. Arabmaldar, Aliasghar & Sahoo, Biresh K. & Ghiyasi, Mojtaba, 2023. "A generalized robust data envelopment analysis model based on directional distance function," European Journal of Operational Research, Elsevier, vol. 311(2), pages 617-632.
    3. Hatami-Marbini, Adel & Arabmaldar, Aliasghar, 2021. "Robustness of Farrell cost efficiency measurement under data perturbations: Evidence from a US manufacturing application," European Journal of Operational Research, Elsevier, vol. 295(2), pages 604-620.
    4. Mohand Bentobache & Mohamed Telli & Abdelkader Mokhtari, 2022. "New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming," Journal of Global Optimization, Springer, vol. 82(4), pages 659-689, April.

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