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A Lifting-Penalty Method for Quadratic Programming with a Quadratic Matrix Inequality Constraint

Author

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  • Wei Liu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116025, China
    School of Applied Mathematics, Beijing Normal University, Zhuhai 519087, China)

  • Li Yang

    (School of Mathematics and Physics Science, Dalian University of Technology, Panjin 124221, China)

  • Bo Yu

    (School of Mathematical Sciences, Dalian University of Technology, Dalian 116025, China)

Abstract

In this paper, a lifting-penalty method for solving the quadratic programming with a quadratic matrix inequality constraint is proposed. Additional variables are introduced to represent the quadratic terms. The quadratic programming is reformulated as a minimization problem having a linear objective function, linear conic constraints and a quadratic equality constraint. A majorization–minimization method is used to solve instead a l 1 penalty reformulation of the minimization problem. The subproblems arising in the method can be solved by using the current semidefinite programming software packages. Global convergence of the method is proven under some suitable assumptions. Some examples and numerical results are given to show that the proposed method is feasible and efficient.

Suggested Citation

  • Wei Liu & Li Yang & Bo Yu, 2020. "A Lifting-Penalty Method for Quadratic Programming with a Quadratic Matrix Inequality Constraint," Mathematics, MDPI, vol. 8(2), pages 1-11, January.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:2:p:153-:d:311733
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    References listed on IDEAS

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    1. Yichuan Ding & Dongdong Ge & Henry Wolkowicz, 2011. "On Equivalence of Semidefinite Relaxations for Quadratic Matrix Programming," Mathematics of Operations Research, INFORMS, vol. 36(1), pages 88-104, February.
    2. Jan Leeuw, 1988. "Convergence of the majorization method for multidimensional scaling," Journal of Classification, Springer;The Classification Society, vol. 5(2), pages 163-180, September.
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