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This paper considers a class of convex constrained nonsmooth convexstochastic composite optimization problems whose objective function is given bythe summation of a differentiable convex component, together with a generalnonsmooth but convex component. The nonsmooth component is not required to haveeasily obtainable proximal operator, or have the max structure that thesmoothing technique in [Nesterov, 2005] can be used. In order to solve suchtype problems, we propose an adaptive smoothing mini-batch stochasticaccelerated gradient (AdaSMSAG) method, which combines the stochasticapproximation method, the Nesterov's accelerated gradient method, and thesmoothing methods that allow general smoothing approximations. Convergence ofthe method is established. Moreover, the order of the worst-case iterationcomplexity is better than that of the state-of-the-art stochastic approximationmethods. Numerical results are provided to illustrate the efficiency of theproposed AdaSMSAG method for a risk management in portfolio optimization and afamily of Wasserstein distributionally robust support vector machine problemswith real data.

Adaptive smoothing mini-batch stochastic accelerated gradient method for nonsmooth convex stochastic composite optimization