A Unified Convergence Analysis of Block Successive Minimization Methods for Nonsmooth Optimization

Understand

The block coordinate descent (BCD) method is widely used for minimizing a continuous function f of several block variables.

• At each iteration of this method, a single block of variables is optimized, while the remaining variables are held fixed.
• To ensure the convergence of the BCD method, the subproblem to be optimized in each iteration needs to be solved exactly to its unique optimal solution.
• Unfortunately, these requirements are often too restrictive for many practical scenarios.