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A parametric linear relaxation algorithm for globally solving nonconvex quadratic programming

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  • Jiao, Hongwei
  • Liu, Sanyang
  • Lu, Nan

Abstract

In this article, we present a parametric linear relaxation algorithm for globally solving the nonconvex quadratic programming (NQP). In this algorithm, a new parametric linearized technique is proposed for generating parametric linear relaxation programming (PLRP) of the NQP, which can be used to determine the lower bound of global minimum value of the NQP. To improve the convergent speed of the proposed algorithm, a pruning operation is employed to compress the investigated region. By subdividing subsequently the initial domain and solving subsequently a series of parametric linear relaxation programming problems over the subdivided domain, the proposed algorithm is convergent to the global minimum of the NQP. Finally, an engineering problem for the design of heat exchanger network and some test examples are used to verify the effectiveness of the proposed algorithm.

Suggested Citation

  • Jiao, Hongwei & Liu, Sanyang & Lu, Nan, 2015. "A parametric linear relaxation algorithm for globally solving nonconvex quadratic programming," Applied Mathematics and Computation, Elsevier, vol. 250(C), pages 973-985.
    • Handle: RePEc:eee:apmaco:v:250:y:2015:i:c:p:973-985
    DOI: 10.1016/j.amc.2014.11.032
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    References listed on IDEAS

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    1. Samuel Burer & Dieter Vandenbussche, 2009. "Globally solving box-constrained nonconvex quadratic programs with semidefinite-based finite branch-and-bound," Computational Optimization and Applications, Springer, vol. 43(2), pages 181-195, June.
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    3. Minyue Fu & Zhi-Quan Luo & Yinyu Ye, 1998. "Approximation Algorithms for Quadratic Programming," Journal of Combinatorial Optimization, Springer, vol. 2(1), pages 29-50, March.
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    5. Peiping Shen & Xiaoai Li, 2013. "Branch-reduction-bound algorithm for generalized geometric programming," Journal of Global Optimization, Springer, vol. 56(3), pages 1123-1142, July.
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    Cited by:

    1. Chenyang Hu & Yuelin Gao & Fuping Tian & Suxia Ma, 2022. "A Relaxed and Bound Algorithm Based on Auxiliary Variables for Quadratically Constrained Quadratic Programming Problem," Mathematics, MDPI, vol. 10(2), pages 1-18, January.
    2. Bo Zhang & YueLin Gao & Xia Liu & XiaoLi Huang, 2023. "Outcome-space branch-and-bound outer approximation algorithm for a class of non-convex quadratic programming problems," Journal of Global Optimization, Springer, vol. 86(1), pages 61-92, May.

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