# A New Inexact Gradient Descent Method with Applications to Nonsmooth Convex Optimization

arXiv: https://arxiv.org/abs/2303.08785 · HTML: https://mlsanity.com/paper/2303.08785/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Mar 2023.

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

- [An Online Feasible Point Method for Benign Generalized Nash Equilibrium Problems](https://mlsanity.com/paper/2410.02400/) (2024)
- [Understanding SAM's Robustness to Noisy Labels through Gradient Down-weighting](https://mlsanity.com/paper/2411.17132/) (2024)

## Abstract (arXiv)

The paper proposes and develops a novel inexact gradient method (IGD) for minimizing C1-smooth functions with Lipschitzian gradients, i.e., for problems of C1,1 optimization. We show that the sequence of gradients generated by IGD converges to zero. The convergence of iterates to stationary points is guaranteed under the Kurdyka- Lojasiewicz (KL) property of the objective function with convergence rates depending on the KL exponent. The newly developed IGD is applied to designing two novel gradient-based methods of nonsmooth convex optimization such as the inexact proximal point methods (GIPPM) and the inexact augmented Lagrangian method (GIALM) for convex programs with linear equality constraints. These two methods inherit global convergence properties from IGD and are confirmed by numerical experiments to have practical advantages over some well-known algorithms of nonsmooth convex optimization.