# Projected Stochastic Gradients for Convex Constrained Problems in Hilbert Spaces

arXiv: https://arxiv.org/abs/1807.09132 · HTML: https://mlsanity.com/paper/1807.09132/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Jul 2018.

## Built on by (most cited first, 2 of 2)

- [Semi-Discrete Optimal Transport: Nearly Minimax Estimation With Stochastic Gradient Descent and Adaptive Entropic Regularization](https://mlsanity.com/paper/2405.14459/) (2024)
- [Decreasing Entropic Regularization Averaged Gradient for Semi-Discrete Optimal Transport](https://mlsanity.com/paper/2510.27340/) (2025)

## Abstract (arXiv)

Convergence of a projected stochastic gradient algorithm is demonstrated for convex objective functionals with convex constraint sets in Hilbert spaces. In the convex case, the sequence of iterates un converges weakly to a point in the set of minimizers with probability one. In the strongly convex case, the sequence converges strongly to the unique optimum with probability one. An application to a class of PDE constrained problems with a convex objective, convex constraint and random elliptic PDE constraints is shown. Theoretical results are demonstrated numerically.