Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions
Abstract
This paper considers the problem of designing accelerated gradient-based algorithms for optimization and saddle-point problems. The class of objective functions is defined by a generalized sector condition. This class of functions contains strongly convex functions with Lipschitz gradients but also non-convex functions, which allows not only to address optimization problems but also saddle-point problems. The proposed design procedure relies on a suitable class of Lyapunov functions and on convex semi-definite programming. The proposed synthesis allows the design of algorithms that reach the performance of state-of-the-art accelerated gradient methods and beyond.
Cite
@article{arxiv.2006.09946,
title = {Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions},
author = {Dennis Gramlich and Christian Ebenbauer and Carsten W. Scherer},
journal= {arXiv preprint arXiv:2006.09946},
year = {2020}
}
Comments
15 pages, 3 figures. This article has been submitted to Systems & Control Letters (https://www.journals.elsevier.com/systems-and-control-letters/)