First Order Methods for Nonsmooth Convex Large-Scale Optimization, II: Utilizing Problem's Structure
Résumé
We present several state-of-the-art First Order methods for "well-structured" large-scale nonsmooth convex programs. In contrast to their "black-boxoriented" prototypes considered in Chapter 1, the methods in question utilize the problem structure in order to convert the original nonsmooth minimization problem into a saddle point problem with smooth convex-concave cost function. This reformulation allows to accelerate signi cantly the solution process. As in Chapter 1, our emphasis is on methods which, under favorable circumstances, exhibit (nearly) dimension-independent convergence rate. Along with investigating the general "well-structured" situation, we outline possibilities to further accelerate First Order methods by randomization.