# Gradient Methods with Regularization for Constrained Optimization Problems and Their Complexity Estimates

## TL;DR

This paper introduces modified gradient and conditional gradient methods for smooth convex optimization in Hilbert spaces, achieving strong convergence and comparable complexity estimates to traditional weakly convergent methods.

## Contribution

It proposes simple, implementable modifications that ensure strong convergence and provide complexity estimates for these optimization methods.

## Key findings

- Achieve strong convergence in convex optimization
- Maintain similar complexity estimates to weakly convergent methods
- Provide practical modifications for gradient-based algorithms

## Abstract

We suggest simple implementable modifications of conditional gradient and gradient projection methods for smooth convex optimization problems in Hilbert spaces. Usually, the custom methods attain only weak convergence. We prove strong convergence of the new versions and establish their complexity estimates, which appear similar to the convergence rate of the weakly convergent versions.