Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions

Dennis Gramlich; Christian Ebenbauer; Carsten W. Scherer

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arXiv · 2006.09946

Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions

Dennis Gramlich·Christian Ebenbauer·Carsten W. Scherer

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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.

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BibTeX RIS

Dennis Gramlich, Christian Ebenbauer, Carsten W. Scherer. 2020-06-17. Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions. https://arxiv.org/abs/2006.09946

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