Constrained Structured Optimization and Augmented Lagrangian Proximal Methods

Abstract: In this talk we discuss finite-dimensional constrained structured optimization problems and explore methods for their numerical solution. Featuring a composite objective function and set-membership constraints, this problem class offers a modeling framework for a variety of applications. A general and flexible algorithm is proposed that interlaces proximal methods and safeguarded augmented Lagrangian schemes. We provide a theoretical characterization of the algorithm and its asymptotic properties, deriving convergence results for fully nonconvex problems. Adopting a proximal gradient method with an oracle as a formal tool, it is demonstrated how the inner subproblems can be solved by off-the-shelf methods for composite optimization, without introducing slack variables and despite the appearance of set-valued projections. Illustrative examples show the versatility of constrained structured programs as a modeling tool and highlight benefits of the implicit approach developed. A preprint paper is available at arXiv:2203.05276.

optimization and control

Audience: researchers in the topic

Variational Analysis and Optimisation Webinar

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