# Convergence Rate of a Penalty Method for Strongly Convex Problems with Linear Constraints

arXiv: https://arxiv.org/abs/2004.13417 · HTML: https://mlsanity.com/paper/2004.13417/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Apr 2020.

## Built on by (most cited first, 1 of 1)

- [Online Poisoning Attack Against Reinforcement Learning under Black-box Environments](https://mlsanity.com/paper/2412.00797/) (2024)

## Abstract (arXiv)

We consider an optimization problem with strongly convex objective and linear inequalities constraints. To be able to deal with a large number of constraints we provide a penalty reformulation of the problem. As penalty functions we use a version of the one-sided Huber losses. The smoothness properties of these functions allow us to choose time-varying penalty parameters in such a way that the incremental procedure with the diminishing step-size converges to the exact solution with the rate O(1/√ k). To the best of our knowledge, we present the first result on the convergence rate for the penalty-based gradient method, in which the penalty parameters vary with time.