ADMM-Based Approach for a Class of Composite Function Optimization Problems

In this study, we optimize a class of composite function problems whose objective function is a sum of three terms: a smooth function, a simple convex function, and a composite function composed of a simple convex function and a linear function. This kind of problem is challenging to solve, as the last two functions are both non-smooth and non-separable. Existing algorithms to solve this type of problem have high computational complexity and cannot deal with large-size problems. To efficiently solve these problems, we first reformulate them as multi-block separable convex minimization problems with linear constraints. Then, we solve the reformulated problem and its dual problem using the alternating direction method of multipliers (ADMM). Finally, we also consider a specific application problem to validate the efficacy of our algorithms. Considering the limitations of existing algorithms, the proposed algorithms are expressly designed to avoid the explosive growth of auxiliary variables and constraints.