We present a convex solution for the design of generalized accelerated gradient algorithms for strongly convex objective functions with Lipschitz continuous gradients. We utilize integral quadratic constraints and the Youla parameterization from robust control theory to formulate a solution of the algorithm design problem as a convex semidefinite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.
%0 Journal Article
%1 SchEbe21
%A Scherer, Carsten
%A Ebenbauer, Christian
%D 2021
%J SIAM Journal on Control and Optimization
%K PN4-3 PN4 EXC2075
%N 6
%P 4615-4645
%R 10.1137/21M1398598
%T Convex Synthesis of Accelerated Gradient Algorithms
%U https://doi.org/10.1137/21M1398598
%V 59
%X We present a convex solution for the design of generalized accelerated gradient algorithms for strongly convex objective functions with Lipschitz continuous gradients. We utilize integral quadratic constraints and the Youla parameterization from robust control theory to formulate a solution of the algorithm design problem as a convex semidefinite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.
@article{SchEbe21,
abstract = {We present a convex solution for the design of generalized accelerated gradient algorithms for strongly convex objective functions with Lipschitz continuous gradients. We utilize integral quadratic constraints and the Youla parameterization from robust control theory to formulate a solution of the algorithm design problem as a convex semidefinite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.},
added-at = {2023-02-24T09:02:33.000+0100},
author = {Scherer, Carsten and Ebenbauer, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/299f778a1f2ca0e057ec43266304d6429/simtech},
doi = {10.1137/21M1398598},
eprint = {https://doi.org/10.1137/21M1398598},
interhash = {998a3878b285a9eba36a03575e2d26e1},
intrahash = {99f778a1f2ca0e057ec43266304d6429},
journal = {SIAM Journal on Control and Optimization},
keywords = {PN4-3 PN4 EXC2075},
number = 6,
pages = {4615-4645},
timestamp = {2024-03-12T10:23:42.000+0100},
title = {Convex Synthesis of Accelerated Gradient Algorithms},
url = {https://doi.org/10.1137/21M1398598},
volume = 59,
year = 2021
}
