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arXiv · 2305.01055

An Augmented Lagrangian Approach to Composite Problems with a Random Linear Operator

Dan Greenstein·Nadav Hallak
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Abstract

We consider the minimization of a sum of a smooth function with a nonsmooth composite function, where the composition is applied on a random linear mapping. This random composite model encompasses many problems, and can especially capture realistic scenarios in which the data is sampled during the optimization process. We propose and analyze a method that combines the classical Augmented Lagrangian framework with a sampling mechanism and adaptive update of the penalty parameter. We show that every accumulation point of the sequence produced by our algorithm is almost surely a critical point.

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Dan Greenstein, Nadav Hallak. 2023-05-01. An Augmented Lagrangian Approach to Composite Problems with a Random Linear Operator. https://arxiv.org/abs/2305.01055

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