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Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints

Author

Listed:
  • Hezhi Luo

    (Zhejiang Sci-Tech University)

  • Xianye Zhang

    (Zhejiang Sci-Tech University)

  • Huixian Wu

    (Hangzhou Dianzi University)

  • Weiqiang Xu

    (Zhejiang Sci-Tech University)

Abstract

We consider in this paper a separable and nonconvex quadratic program (QP) with a quadratic constraint and a box constraint that arises from application in optimal portfolio deleveraging (OPD) in finance and is known to be NP-hard. We first propose an improved Lagrangian breakpoint search algorithm based on the secant approach (called ILBSSA) for this nonconvex QP, and show that it converges to either a suboptimal solution or a global solution of the problem. We then develop a successive convex optimization (SCO) algorithm to improve the quality of suboptimal solutions derived from ILBSSA, and show that it converges to a KKT point of the problem. Second, we develop a new global algorithm (called ILBSSA-SCO-BB), which integrates the ILBSSA and SCO methods, convex relaxation and branch-and-bound framework, to find a globally optimal solution to the underlying QP within a pre-specified $$\epsilon $$ ϵ -tolerance. We establish the convergence of the ILBSSA-SCO-BB algorithm and its complexity. Preliminary numerical results are reported to demonstrate the effectiveness of the ILBSSA-SCO-BB algorithm in finding a globally optimal solution to large-scale OPD instances.

Suggested Citation

  • Hezhi Luo & Xianye Zhang & Huixian Wu & Weiqiang Xu, 2023. "Effective algorithms for separable nonconvex quadratic programming with one quadratic and box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 199-240, September.
    • Handle: RePEc:spr:coopap:v:86:y:2023:i:1:d:10.1007_s10589-023-00485-0
    DOI: 10.1007/s10589-023-00485-0
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    References listed on IDEAS

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    1. Xiaodong Ding & Hezhi Luo & Huixian Wu & Jianzhen Liu, 2021. "An efficient global algorithm for worst-case linear optimization under uncertainties based on nonlinear semidefinite relaxation," Computational Optimization and Applications, Springer, vol. 80(1), pages 89-120, September.
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