# Convex Synthesis of Accelerated Gradient Algorithms

arXiv: https://arxiv.org/abs/2102.06520 · HTML: https://mlsanity.com/paper/2102.06520/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Feb 2021.

## Built on by (most cited first, 4 of 4)

- [Learning to optimize with convergence guarantees using nonlinear system theory](https://mlsanity.com/paper/2403.09389/) (2024)
- [Learning to optimize with guarantees: a complete characterization of linearly convergent algorithms](https://mlsanity.com/paper/2508.00775/) (2025)
- [On Centralized and Distributed Mirror Descent: Convergence Analysis Using Quadratic Constraints](https://mlsanity.com/paper/2105.14385/) (2021)
- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)

## Abstract (arXiv)

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.