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IPRQP: a primal-dual interior-point relaxation algorithm for convex quadratic programming

Author

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  • Rui-Jin Zhang

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

  • Xin-Wei Liu

    (Hebei University of Technology)

  • Yu-Hong Dai

    (Chinese Academy of Sciences
    University of Chinese Academy of Sciences)

Abstract

We propose IPRQP, an enhanced primal-dual interior-point relaxation method (IPRM), for solving convex quadratic programming. This method is based on a smoothing barrier augmented Lagrangian function for convex quadratic programming. IPRQP inherits the advantages of IPRM, including not requiring iterative points to be interior points, which makes IPRQP suitable for the warm-starting of combinatorial optimization problems. Compared to IPRM, the customized starting points allow the line search of IPRQP to contain only vector operations. In addition, IPRQP improves the updating scheme of the barrier parameter and provides a certificate of infeasibility. Some results on global convergence are presented. We implement the algorithm on convex quadratic programming problems from Maros-Mészaros and the benchmark problem sets NETLIB and Kennington, which contain feasible and infeasible linear programming problems. The numerical results show that our algorithm is reliable for feasible problems and efficient for detecting the infeasibility of infeasible problems.

Suggested Citation

  • Rui-Jin Zhang & Xin-Wei Liu & Yu-Hong Dai, 2023. "IPRQP: a primal-dual interior-point relaxation algorithm for convex quadratic programming," Journal of Global Optimization, Springer, vol. 87(2), pages 1027-1053, November.
    • Handle: RePEc:spr:jglopt:v:87:y:2023:i:2:d:10.1007_s10898-023-01314-8
    DOI: 10.1007/s10898-023-01314-8
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    References listed on IDEAS

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    1. Goran Banjac & Paul Goulart & Bartolomeo Stellato & Stephen Boyd, 2019. "Infeasibility Detection in the Alternating Direction Method of Multipliers for Convex Optimization," Journal of Optimization Theory and Applications, Springer, vol. 183(2), pages 490-519, November.
    2. Spyridon Pougkakiotis & Jacek Gondzio, 2021. "An interior point-proximal method of multipliers for convex quadratic programming," Computational Optimization and Applications, Springer, vol. 78(2), pages 307-351, March.
    3. Jacek Gondzio, 2012. "Matrix-free interior point method," Computational Optimization and Applications, Springer, vol. 51(2), pages 457-480, March.
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