Convergence for nonconvex ADMM, with applications to CT imaging

The alternating direction method of multipliers (ADMM) algorithm is a powerful and flexible tool for complex optimization problems of the form $\min\{f(x)+g(y) : Ax+By=c\}$. ADMM exhibits robust empirical performance across a range of challenging settings including nonsmoothness and nonconvexity of the objective functions $f$ and $g$, and provides a simple and natural approach to the inverse problem of image reconstruction for computed tomography (CT) imaging. From the theoretical point of view, existing results for convergence in the nonconvex setting generally …

algorithm applications convergence form functions imaging optimization performance robust simple tool