Alternating Forward–backward Splitting for Linearly Constrained Optimization Problems

We present an alternating forward–backward splitting method for solving linearly constrained structured optimization problems. The algorithm takes advantage of the separable structure and possibly asymmetric regularity properties of the objective functions involved. We also describe some applications to the study of non-Newtonian fluids and image reconstruction problems. We conclude with a numerical example, and its comparison with Condat’s algorithm. An acceleration heuristic is also briefly outlined.