Adaptive splitting algorithms for the sum of operators

Abstract: A general optimization problem can often be reduced to finding a zero of a sum of multiple (maximally) monotone operators, which creates challenging computational tasks as a whole. It motivates the development of splitting algorithms in order to simplify the computations by dealing with each operator separately, hence the name "splitting". Some of the most successful splitting algorithms in applications are the forward-backward algorithm, the Douglas-Rachford algorithm, and the alternating directions method of multipliers (ADMM). In this talk, we discuss some adaptive splitting algorithms for finding a zero of the sum of operators. The main idea is to adapt the algorithm parameters to the generalized monotonicity of the operators so that the generated sequence converges to a fixed point.

optimization and control

Audience: researchers in the topic

Variational Analysis and Optimisation Webinar

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