New gradient sliding results on convex optimization with smoothness structure

Applied and Computational Mathematics Seminar
Monday, April 3, 2023 - 2:00pm for 1 hour (actually 50 minutes)
Skiles 005 and
Yuyuan Ouyang – Clemson University – yuyuano@clemson.edu
Wenjing Liao

In this talk, we present new gradient sliding results for constrained convex optimization with applications in image reconstruction and decentralized distributed optimization. Specifically, we will study classes of large-scale problems that minimizes a convex objective function over feasible set with linear constraints. We will show that by exploring the gradient sliding technique, the number of gradient evaluations of the objective function can be reduced by exploring the smoothness structure. Our results could lead to new decentralized algorithms for multi-agent optimization with graph topology invariant gradient/sampling complexity and new ADMM algorithms for solving total variation image reconstruction problems with accelerated gradient complexity.