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New LP-based local and global algorithms for continuous and mixed-integer nonconvex quadratic programming

Author

Listed:
  • Mohand Bentobache

    (University of Laghouat)

  • Mohamed Telli

    (University of Laghouat)

  • Abdelkader Mokhtari

    (University of Laghouat)

Abstract

In this work, we propose a new approach called “Successive Linear Programming Algorithm (SLPA)” for finding an approximate global minimizer of general nonconvex quadratic programs. This algorithm can be initialized by any extreme point of the convex polyhedron of the feasible domain. Furthermore, we generalize the simplex algorithm for finding a local minimizer of concave quadratic programs written in standard form. We prove a new necessary and sufficient condition for local optimality, then we describe the Revised Primal Simplex Algorithm (RPSA). Finally, we propose a hybrid local-global algorithm called “SLPLEX”, which combines RPSA with SLPA for solving general concave quadratic programs. In order to compare the proposed algorithms to the branch-and-bound algorithm of CPLEX12.8 and the branch-and-cut algorithm of Quadproga, we develop an implementation with MATLAB and we present numerical experiments on 139 nonconvex quadratic test problems.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:4:d:10.1007_s10898-021-01108-w
    DOI: 10.1007/s10898-021-01108-w
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    References listed on IDEAS

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    2. Tao Pham Dinh & Nam Nguyen Canh & Hoai Le Thi, 2010. "An efficient combined DCA and B&B using DC/SDP relaxation for globally solving binary quadratic programs," Journal of Global Optimization, Springer, vol. 48(4), pages 595-632, December.
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    5. Hoang Tuy, 2016. "Convex Analysis and Global Optimization," Springer Optimization and Its Applications, Springer, edition 2, number 978-3-319-31484-6, June.
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