A Lyapunov perspective to projection algorithms

Abstract: The operator theoretic point of view has been very successful in the study of iterative splitting methods under a unified framework. These algorithms include the Method of Alternating Projections as well as the Douglas-Rachford Algorithm, which is dual to the Alternating Direction Method of Multipliers, and they allow nice geometric interpretations. While convergence results for these algorithms have been known for decades when problems are convex, for non-convex problems progress on convergence results has significantly increased once arguments based on Lyapunov functions were used. In this talk we give an overview of the underlying techniques in Lyapunov's direct method and look at convergence of iterative projection methods through this lens.

optimization and control

Audience: researchers in the topic

Variational Analysis and Optimisation Webinar

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