A class of algorithms for constrained stochastic convex optimization with sparsity

Abstract This work develops a class of algorithms for stochastic convex optimization (SCO) with sparsity. Our objective function is based on the empirical risk of stochastic convex optimization with constraints, where the weights are adopted in the optimization variables of terms. It is established that the approximation sequence generated by our algorithms has the oracle properties. That is, (i) the sets of the zero and nonzero components of the minima of SCO can be correctly identified with probability one using a finite number of sampling data and approximations, and (ii) the nonzero components converge almost surely to the true values together with the desired asymptotic distribution. The effectiveness of our algorithms is validated by numerical experiments.