# Adaptive Mirror Descent for Constrained Optimization

## TL;DR

This paper introduces an adaptive Mirror Descent method for constrained convex optimization that improves convergence rates and can generate dual solutions, especially effective for strongly convex problems.

## Contribution

The paper proposes an adaptive stepsize Mirror Descent algorithm with enhanced convergence rates and dual solution generation capabilities for constrained convex optimization.

## Key findings

- Improved convergence rate over fixed stepsize MD
- Method generates dual solutions for certain constraints
- Effective restart technique for strongly convex problems

## Abstract

This paper seeks to address how to solve non-smooth convex and strongly convex optimization problems with functional constraints. The introduced Mirror Descent (MD) method with adaptive stepsizes is shown to have a better convergence rate than MD with fixed stepsizes due to the improved constant. For certain types of constraints, the method is proved to generate dual solution. For the strongly convex case, the restart technique is applied.