A single cut proximal bundle method for stochastic convex composite optimization

In this paper, we consider optimization problems where the objective is the sum of a function given by an expectation and a closed convex composite function. For such problems, we propose a stochastic composite proximal bundle (SCPB) method with optimal complexity. The method does not require estimation of parameters involved in the assumptions on the … Read more

A proximal bundle variant with optimal iteration-complexity for a large range of prox stepsizes

This paper presents a proximal bundle variant, namely, the relaxed proximal bundle (RPB) method, for solving convex nonsmooth composite optimization problems. Like other proximal bundle variants, RPB solves a sequence of prox bundle subproblems whose objective functions are regularized composite cutting-plane models. Moreover, RPB uses a novel condition to decide whether to perform a serious … Read more