Stochastic Difference-of-Convex Algorithms for Solving nonconvex optimization problems
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The paper deals with stochastic difference-of-convex functions programs, that is, optimization problems whose cost function is a sum of a lower semicontinuous difference-of-convex function and the expectation of a stochastic difference-of-convex function with respect to a probability distribution. This class of nonsmooth and nonconvex stochastic optimization problems plays a central role in many practical applications. While in the literature there are many contributions dealing with convex and/or smooth stochastic optimizations problems, there is still a few algorithms dealing with nonconvex and nonsmooth programs. In deterministic optimization literature, the Difference-of-Convex functions Algorithm (DCA) is recognized to be one of a few algorithms to solve effectively nonconvex and nonsmooth optimization problems. The main purpose of this paper is to present some new stochastic variants of DCA for solving stochastic difference-of-convex functions programs. The convergence analysis of the proposed algorithms are carefully studied.
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