Abstract. We propose an inexact primal-dual smoothing framework to solve a strongly-convexgenerally-concave saddle point problem with non-bilinear structure, with potentially a large number of component functions. We develop a probabilistic version of our smoothing framework, which allows each sub-problem to be solved by randomized algorithms inexactly in expectation. In addition, we extend both our deterministic and probabilistic frameworks to solve generally convex-concave saddle point problems. Compared to the existing approaches, our frameworks enjoy superior first-order oracle complexities, and can easily exploit additional regularities in the problem. As an important application, we illustrate the efficacy of our frameworks on the large-scale convex constrained optimization problems.
In REF , an inexact primal-dual smoothing framework is developed for large-scale non-bilinear saddle point problems, in which randomized algorithms are used to solve the primal and dual subproblems.
An Inexact Primal-Dual Smoothing Framework for Large-Scale Non-Bilinear Saddle Point Problems
arXiv: Optimization and Control
Mathematics