%0 Journal Article %1 GraEbe21 %A Gramlich, Dennis %A Ebenbauer, Christian %A Scherer, Carsten W. %D 2022 %J Systems & Control Letters %K EXC2075 PN4 PN4-3 selected %R 10.1016/j.sysconle.2022.105271 %T Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions %U https://doi.org/10.1016/j.sysconle.2022.105271 %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 = {2024-03-26T11:56:41.000+0100}, author = {Gramlich, Dennis and Ebenbauer, Christian and Scherer, Carsten W.}, biburl = {https://puma.ub.uni-stuttgart.de/bibtex/2175f2fc9bd1e64078b90b253a6d6596d/exc2075}, 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 = {175f2fc9bd1e64078b90b253a6d6596d}, journal = {Systems & Control Letters}, keywords = {EXC2075 PN4 PN4-3 selected}, timestamp = {2024-03-27T16:19:07.000+0100}, title = {Synthesis of Accelerated Gradient Algorithms for Optimization and Saddle Point Problems using Lyapunov functions}, url = {https://doi.org/10.1016/j.sysconle.2022.105271}, volume = 165, year = 2022 }