Accelerated Alternating Descent Methods for Dykstra-Like Problems

This paper extends recent results by the first author and T. Pock (ICG, TU Graz, Austria) on the acceleration of alternating minimization techniques for quadratic plus nonsmooth objectives depending on two variables. We discuss here the strongly convex situation, and how ‘fast’ methods can be derived by adapting the overrelaxation strategy of Nesterov for projected gradient descent. We also investigate slightly more general alternating descent methods, where several descent steps in each variable are alternatively performed.