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Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints

Author

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  • Weiwei Kong

    (Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37830)

  • Jefferson G. Melo

    (Instituto de Matemática e Estatística, Universidade Federal de Goiás, Goiânia, Goiás 74001-970, Brazil)

  • Renato D. C. Monteiro

    (School of Industrial and Systems Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332)

Abstract

This paper proposes and analyzes a proximal augmented Lagrangian (NL-IAPIAL) method for solving constrained nonconvex composite optimization problems, where the constraints are smooth and convex with respect to the order given by a closed convex cone. Each NL-IAPIAL iteration consists of inexactly solving a proximal augmented Lagrangian subproblem by an accelerated composite gradient method followed by a Lagrange multiplier update. Under some mild assumptions, a complexity bound for NL-IAPIAL to obtain an approximate stationary solution of the problem is also derived. Numerical experiments are also given to illustrate the computational efficiency of the proposed method.

Suggested Citation

  • Weiwei Kong & Jefferson G. Melo & Renato D. C. Monteiro, 2023. "Iteration Complexity of a Proximal Augmented Lagrangian Method for Solving Nonconvex Composite Optimization Problems with Nonlinear Convex Constraints," Mathematics of Operations Research, INFORMS, vol. 48(2), pages 1066-1094, May.
    • Handle: RePEc:inm:ormoor:v:48:y:2023:i:2:p:1066-1094
    DOI: 10.1287/moor.2022.1301
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