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On how to solve large-scale log-determinant optimization problems

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  • Chengjing Wang

    (Southwest Jiaotong University)

Abstract

We propose a proximal augmented Lagrangian method and a hybrid method, i.e., employing the proximal augmented Lagrangian method to generate a good initial point and then employing the Newton-CG augmented Lagrangian method to get a highly accurate solution, to solve large-scale nonlinear semidefinite programming problems whose objective functions are a sum of a convex quadratic function and a log-determinant term. We demonstrate that the algorithms can supply a high quality solution efficiently even for some ill-conditioned problems.

Suggested Citation

  • Chengjing Wang, 2016. "On how to solve large-scale log-determinant optimization problems," Computational Optimization and Applications, Springer, vol. 64(2), pages 489-511, June.
    • Handle: RePEc:spr:coopap:v:64:y:2016:i:2:d:10.1007_s10589-015-9812-y
    DOI: 10.1007/s10589-015-9812-y
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    References listed on IDEAS

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    1. Defeng Sun, 2006. "The Strong Second-Order Sufficient Condition and Constraint Nondegeneracy in Nonlinear Semidefinite Programming and Their Implications," Mathematics of Operations Research, INFORMS, vol. 31(4), pages 761-776, November.
    2. Zhaolin Hu & Jing Cao & L. Jeff Hong, 2012. "Robust Simulation of Global Warming Policies Using the DICE Model," Management Science, INFORMS, vol. 58(12), pages 2190-2206, December.
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    Cited by:

    1. Chengjing Wang & Peipei Tang, 2017. "A primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming," Computational Optimization and Applications, Springer, vol. 68(3), pages 503-532, December.
    2. Takashi Nakagaki & Mituhiro Fukuda & Sunyoung Kim & Makoto Yamashita, 2020. "A dual spectral projected gradient method for log-determinant semidefinite problems," Computational Optimization and Applications, Springer, vol. 76(1), pages 33-68, May.

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