# Robust and structure exploiting optimization algorithms: An integral quadratic constraint approach

arXiv: https://arxiv.org/abs/1905.00279 · HTML: https://mlsanity.com/paper/1905.00279/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 May 2019.

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

- [Convex Programs and Lyapunov Functions for Reinforcement Learning: A Unified Perspective on the Analysis of Value-Based Methods](https://mlsanity.com/paper/2202.06922/) (2022)
- [Transient growth of accelerated optimization algorithms](https://mlsanity.com/paper/2103.08017/) (2021)
- [Tradeoffs between convergence rate and noise amplification for momentum-based accelerated optimization algorithms](https://mlsanity.com/paper/2209.11920/) (2022)
- [Online Convex Optimization and Integral Quadratic Constraints: An automated approach to regret analysis](https://mlsanity.com/paper/2503.23600/) (2025)

## Abstract (arXiv)

We consider the problem of analyzing and designing gradient-based discrete-time optimization algorithms for a class of unconstrained optimization problems having strongly convex objective functions with Lipschitz continuous gradient. By formulating the problem as a robustness analysis problem and making use of a suitable adaptation of the theory of integral quadratic constraints, we establish a framework that allows to analyze convergence rates and robustness properties of existing algorithms and enables the design of novel robust optimization algorithms with prespecified guarantees capable of exploiting additional structure in the objective function.