A Coordinate Gradient Descent Method for Nonsmooth Nonseparable Minimization

This paper presents a coordinate gradient descent approach for minimizing the sum of a smooth function and a nonseparable convex function. We find a search direction by solving a subproblem obtained by a second-order approximation of the smooth function and adding a separable convex function. Under a local Lipschitzian error bound assumption, we show that the algorithm possesses global and local linear convergence properties. We also give some numerical tests (including image recovery examples) to illustrate the efficiency of the proposed method.