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Augmented Lagrangian method for second-order cone programs under second-order sufficiency

Author

Listed:
  • Nguyen T. V. Hang

    (Wayne State University
    Vietnam Academy of Science and Technology)

  • Boris S. Mordukhovich

    (Wayne State University)

  • M. Ebrahim Sarabi

    (Miami University)

Abstract

This paper addresses problems of second-order cone programming important in optimization theory and applications. The main attention is paid to the augmented Lagrangian method (ALM) for such problems considered in both exact and inexact forms. Using generalized differential tools of second-order variational analysis, we formulate the corresponding version of second-order sufficiency and use it to establish, among other results, the uniform second-order growth condition for the augmented Lagrangian. The latter allows us to justify the solvability of subproblems in the ALM and to prove the linear primal–dual convergence of this method.

Suggested Citation

  • Nguyen T. V. Hang & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2022. "Augmented Lagrangian method for second-order cone programs under second-order sufficiency," Journal of Global Optimization, Springer, vol. 82(1), pages 51-81, January.
    • Handle: RePEc:spr:jglopt:v:82:y:2022:i:1:d:10.1007_s10898-021-01068-1
    DOI: 10.1007/s10898-021-01068-1
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    References listed on IDEAS

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    1. A. Izmailov & A. Kurennoy & M. Solodov, 2015. "Local convergence of the method of multipliers for variational and optimization problems under the noncriticality assumption," Computational Optimization and Applications, Springer, vol. 60(1), pages 111-140, January.
    2. Alexander Shapiro & Jie Sun, 2004. "Some Properties of the Augmented Lagrangian in Cone Constrained Optimization," Mathematics of Operations Research, INFORMS, vol. 29(3), pages 479-491, August.
    3. Ashkan Mohammadi & Boris S. Mordukhovich & M. Ebrahim Sarabi, 2020. "Superlinear Convergence of the Sequential Quadratic Method in Constrained Optimization," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 731-758, September.
    4. R. Tyrrell Rockafellar, 1989. "Second-Order Optimality Conditions in Nonlinear Programming Obtained by Way of Epi-Derivatives," Mathematics of Operations Research, INFORMS, vol. 14(3), pages 462-484, August.
    5. E. G. Birgin & G. Haeser & A. Ramos, 2018. "Augmented Lagrangians with constrained subproblems and convergence to second-order stationary points," Computational Optimization and Applications, Springer, vol. 69(1), pages 51-75, January.
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    Cited by:

    1. Pham Duy Khanh & Boris S. Mordukhovich & Vo Thanh Phat & Dat Ba Tran, 2023. "Generalized damped Newton algorithms in nonsmooth optimization via second-order subdifferentials," Journal of Global Optimization, Springer, vol. 86(1), pages 93-122, May.
    2. Nguyen Huy Chieu & Nguyen Thi Quynh Trang & Ha Anh Tuan, 2022. "Quadratic Growth and Strong Metric Subregularity of the Subdifferential for a Class of Non-prox-regular Functions," Journal of Optimization Theory and Applications, Springer, vol. 194(3), pages 1081-1106, September.

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