# Almost surely constrained convex optimization

arXiv: https://arxiv.org/abs/1902.00126 · HTML: https://mlsanity.com/paper/1902.00126/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jan 2019.

## Built on by (most cited first, 3 of 3)

- [Zeroth and First Order Stochastic Frank-Wolfe Algorithms for Constrained Optimization](https://mlsanity.com/paper/2107.06534/) (2021)
- [Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization](https://mlsanity.com/paper/2202.13212/) (2022)
- [Randomized Feasibility Methods for Constrained Optimization with Adaptive Step Sizes](https://mlsanity.com/paper/2601.20076/) (2026)

## Abstract (arXiv)

We propose a stochastic gradient framework for solving stochastic composite convex optimization problems with (possibly) infinite number of linear inclusion constraints that need to be satisfied almost surely. We use smoothing and homotopy techniques to handle constraints without the need for matrix-valued projections. We show for our stochastic gradient algorithm O(log(k)/√k) convergence rate for general convex objectives and O(log(k)/k) convergence rate for restricted strongly convex objectives. These rates are known to be optimal up to logarithmic factors, even without constraints. We demonstrate the performance of our algorithm with numerical experiments on basis pursuit, a hard margin support vector machines and a portfolio optimization and show that our algorithm achieves state-of-the-art practical performance.