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On a primal-dual Newton proximal method for convex quadratic programs

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  • Alberto Marchi

    (Universität der Bundeswehr München)

Abstract

This paper introduces QPDO, a primal-dual method for convex quadratic programs which builds upon and weaves together the proximal point algorithm and a damped semismooth Newton method. The outer proximal regularization yields a numerically stable method, and we interpret the proximal operator as the unconstrained minimization of the primal-dual proximal augmented Lagrangian function. This allows the inner Newton scheme to exploit sparse symmetric linear solvers and multi-rank factorization updates. Moreover, the linear systems are always solvable independently from the problem data and exact linesearch can be performed. The proposed method can handle degenerate problems, provides a mechanism for infeasibility detection, and can exploit warm starting, while requiring only convexity. We present details of our open-source C implementation and report on numerical results against state-of-the-art solvers. QPDO proves to be a simple, robust, and efficient numerical method for convex quadratic programming.

Suggested Citation

  • Alberto Marchi, 2022. "On a primal-dual Newton proximal method for convex quadratic programs," Computational Optimization and Applications, Springer, vol. 81(2), pages 369-395, March.
    • Handle: RePEc:spr:coopap:v:81:y:2022:i:2:d:10.1007_s10589-021-00342-y
    DOI: 10.1007/s10589-021-00342-y
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    References listed on IDEAS

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    Cited by:

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    2. Shaoze Li & Zhibin Deng & Cheng Lu & Junhao Wu & Jinyu Dai & Qiao Wang, 2023. "An efficient global algorithm for indefinite separable quadratic knapsack problems with box constraints," Computational Optimization and Applications, Springer, vol. 86(1), pages 241-273, September.

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