%0 Journal Article %1 GraEbe21 %A Gramlich, Dennis %A Ebenbauer, Christian %A Scherer, Carsten W. %D 2022 %J Syst. Control Lett. %K PN4-3 PN4 curated EXC2075 %R 10.1016/j.sysconle.2022.105271 %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 = {2023-11-02T08:49:31.000+0100}, author = {Gramlich, Dennis and Ebenbauer, Christian and Scherer, Carsten W.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2eed17d11f2addc5db2ba5c6287c35f7d/simtech}, doi = {10.1016/j.sysconle.2022.105271}, eprint = {2006.09946}, eprintclass = {math.OC}, eprinttype = {arXiv}, file = {:GraEbe20 - Convex Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems Using Lyapunov Functions.pdf:PDF}, interhash = {5b4472847c14de83890cec5450738518}, intrahash = {eed17d11f2addc5db2ba5c6287c35f7d}, journal = {Syst. Control Lett. }, keywords = {PN4-3 PN4 curated EXC2075}, timestamp = {2024-03-12T10:23:38.000+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 }