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 semi-definite 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 J. Contr. Optim. (to appear)
%K PN4-3 PN4 EXC2075 IMNG
%T Convex Synthesis of Accelerated Gradient Algorithms
%U https://arxiv.org/abs/2102.06520
%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 semi-definite 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 semi-definite program. We establish explicit formulas for the optimal convergence rates and extend the proposed synthesis solution to extremum control problems.},
added-at = {2024-03-12T10:23:39.000+0100},
author = {Scherer, Carsten and Ebenbauer, Christian},
biburl = {https://puma.ub.uni-stuttgart.de/bibtex/28cbbbd4a9f6a93d323a3e92103b747a9/mst},
eprint = {2102.06520},
eprintclass = {math.OC},
eprinttype = {arXiv},
file = {:SchEbe21 - Convex Synthesis of Accelerated Gradient Algorithms.pdf:PDF},
interhash = {998a3878b285a9eba36a03575e2d26e1},
intrahash = {8cbbbd4a9f6a93d323a3e92103b747a9},
journal = {SIAM J. Contr. Optim. (to appear)},
keywords = {PN4-3 PN4 EXC2075 IMNG},
timestamp = {2024-03-12T10:23:39.000+0100},
title = {Convex Synthesis of Accelerated Gradient Algorithms},
url = {https://arxiv.org/abs/2102.06520},
year = 2021
}