# Proximal Gradient

> Source: https://sukruyusufkaya.com/en/glossary/proximal-gradient
> Updated: 2026-05-13T20:01:42.014Z
> Type: glossary
> Category: matematik-istatistik-optimizasyon
**TLDR:** An optimization method used for problems that combine smooth and non-smooth objective components.

<p>The proximal gradient method is used especially when an objective function contains both a smooth differentiable part and a sharp or non-smooth component. Terms such as L1 regularization, which encourage sparsity, are classic examples. The method combines a standard gradient step with a proximal operator to produce solutions. This allows optimization while also preserving certain structural properties. It is particularly valuable in sparse modeling and modern regularized optimization problems.</p>