# Accelerated Algorithms for a Class of Optimization Problems with Equality and Box Constraints

arXiv: https://arxiv.org/abs/2305.04433 · HTML: https://mlsanity.com/paper/2305.04433/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 21 references that are in the map.
- First posted on arXiv 8 May 2023.

## Builds on (most cited first, 10 of 10)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [A Differential Equation for Modeling Nesterov's Accelerated Gradient Method: Theory and Insights](https://mlsanity.com/paper/1503.01243/) (2015)
- [DC3: A learning method for optimization with hard constraints](https://mlsanity.com/paper/2104.12225/) (2021)
- [Neural Networks are Convex Regularizers: Exact Polynomial-time Convex Optimization Formulations for Two-layer Networks](https://mlsanity.com/paper/2002.10553/) (2020)
- [DeepOPF: A Deep Neural Network Approach for Security-Constrained DC Optimal Power Flow](https://mlsanity.com/paper/1910.14448/) (2019)
- [DeepOPF: Deep Neural Network for DC Optimal Power Flow](https://mlsanity.com/paper/1905.04479/) (2019)
- [Accelerated first-order primal-dual proximal methods for linearly constrained composite convex programming](https://mlsanity.com/paper/1606.09155/) (2016)
- [A Stable High-order Tuner for General Convex Functions](https://mlsanity.com/paper/2011.09996/) (2020)
- [Nesterov Acceleration for Equality-Constrained Convex Optimization via Continuously Differentiable Penalty Functions](https://mlsanity.com/paper/2103.06494/) (2021)
- [Accelerated Algorithms for a Class of Optimization Problems with Constraints](https://mlsanity.com/paper/2205.00583/) (2022)

## Abstract (arXiv)

Convex optimization with equality and inequality constraints is a ubiquitous problem in several optimization and control problems in large-scale systems. Recently there has been a lot of interest in establishing accelerated convergence of the loss function. A class of high-order tuners was recently proposed in an effort to lead to accelerated convergence for the case when no constraints are present. In this paper, we propose a new high-order tuner that can accommodate the presence of equality constraints. In order to accommodate the underlying box constraints, time-varying gains are introduced in the high-order tuner which leverage convexity and ensure anytime feasibility of the constraints. Numerical examples are provided to support the theoretical derivations.