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arXiv · 2307.15627

Convergence of Augmented Lagrangian Methods for Composite Optimization Problems

Nguyen T. V. Hang·Ebrahim Sarabi
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Abstract

Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property, called the semi-stability of second subderivatives, and demonstrate that it is widely satisfied for numerous classes of functions, important for applications in constrained and composite optimization problems. Using the latter condition and a certain second-order sufficient condition, we are able to establish Q-linear convergence of the primal-dual sequence for an inexact version of the ALM for composite programs.

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Nguyen T. V. Hang, Ebrahim Sarabi. 2023-07-28. Convergence of Augmented Lagrangian Methods for Composite Optimization Problems. https://arxiv.org/abs/2307.15627

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