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A primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming

Author

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  • Chengjing Wang

    (Southwest Jiaotong University)

  • Peipei Tang

    (Zhejiang University City College)

Abstract

In this paper, we propose a primal majorized semismooth Newton-CG augmented Lagrangian method for large-scale linearly constrained convex programming problems, especially for some difficult problems. The basic idea of this method is to apply the majorized semismooth Newton-CG augmented Lagrangian method to the primal convex problem. And we take two special nonlinear semidefinite programming problems as examples to illustrate the algorithm. Furthermore, we establish the global convergence and the iteration complexity of the algorithm. Numerical experiments demonstrate that our method works very well for the testing problems, especially for many ill-conditioned ones.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:coopap:v:68:y:2017:i:3:d:10.1007_s10589-017-9930-9
    DOI: 10.1007/s10589-017-9930-9
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    References listed on IDEAS

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    1. DEVOLDER, Olivier & GLINEUR, François & NESTEROV, Yurii, 2011. "First-order methods of smooth convex optimization with inexact oracle," LIDAM Discussion Papers CORE 2011002, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. 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.
    3. R. T. Rockafellar, 1976. "Augmented Lagrangians and Applications of the Proximal Point Algorithm in Convex Programming," Mathematics of Operations Research, INFORMS, vol. 1(2), pages 97-116, May.
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