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Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems by Ouyang, Hui is a scholarly article available to read on EtoBox.

What is Alternating Proximity Mapping Method for Convex-Concave Saddle-Point Problems about?

We proposed an iterate scheme for solving convex-concave saddle-point problems associated with general convex-concave functions. We demonstrated that when our iterate scheme is applied to a special class of convex-concave functions, which are constructed by a bilinear coupling term plus a difference of two convex functions, it becomes a generalization of several popular primal-dual algorithms from constant involved parameters to involved parameters as general sequences. For this specific class of convex-concave functions, we proved that the sequence of function values, taken over the averages of iterates generated by our scheme, converges to the value of the function at a saddle-point. Additionally, we provided convergence results for both the sequence of averages of our iterates and the sequence of our iterates. In our numerical experiments, we implemented our algorithm in a matrix game, a linear program in inequality form, and a least-squares problem with $\ell_{1}$ regularization. In these examples, we also compared our algorithm with other primal-dual algorithms where parameters in their iterate schemes were kept constant. Our experimental results not only validated our theoret

Author

Ouyang, Hui

Published

2023

Language

EN