# Proximal Gradient Descent and Proximal Coordinate descent for Lasso Problem

Why is proximal coordinate descent much less affected by bad conditioning than proximal gradient descent?

For example, we can consider this problem : $$\min_x \frac{1}{2}\|Ax-b\|^2_2 + \lambda\|x\|_1$$

If A has a large condition number, how can we demonstrate that the algorithm of proximal coordinate descent is much less affected than proximal gradient?