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.
:GraEbe21 - Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems Using Lyapunov Functions.pdf:PDF;:GraEbe21 - Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems Using Lyapunov Functions.bib:bib
%0 Journal Article
%1 GraEbe21
%A Gramlich, Dennis
%A Ebenbauer, Christian
%A Scherer, Carsten W.
%D 2022
%J Syst. Control Lett.
%K from:carsten.scherer pn4 peerReviewed EXC2075 imng
%T Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions
%U https://arxiv.org/abs/2006.09946
%V 165
%X 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.
@article{GraEbe21,
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.},
added-at = {2023-02-24T09:02:33.000+0100},
archiveprefix = {arXiv},
author = {Gramlich, Dennis and Ebenbauer, Christian and Scherer, Carsten W.},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/29f9e3046f56c3481e078bf0606f28226/mathematik},
eprint = {2006.09946},
file = {:GraEbe21 - Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems Using Lyapunov Functions.pdf:PDF;:GraEbe21 - Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems Using Lyapunov Functions.bib:bib},
interhash = {5b4472847c14de83890cec5450738518},
intrahash = {9f9e3046f56c3481e078bf0606f28226},
journal = {Syst. Control Lett.},
keywords = {from:carsten.scherer pn4 peerReviewed EXC2075 imng},
primaryclass = {math.OC},
timestamp = {2024-03-12T10:23:56.000+0100},
title = {Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions},
url = {https://arxiv.org/abs/2006.09946},
volume = 165,
year = 2022
}