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Stochastic first- and zeroth-order methods for nonconvex stochastic programming. (English) Zbl 1295.90026
A randomized stochastic gradient method for solving unconstrained expectation type stochastic programs with noisy function values or gradients of the objective function is introduced. The theoretical results aim at problems with a nonconvex objective function f which may occur e.g. in case of endogenous uncertainty and in simulation-based optimization. The authors study convergence properties of the suggested algorithms, such as the rate of convergence which is nearly optimal for convex problems, improvements of large deviation results without independence assumption or strategy for selection step sizes. By means of Gaussian smoothing approximation of f the algorithms are extended to solving a class of simulation-based optimization problems in which only stochastic zero-order information is available. No numerical experience with the proposed methods is reported.

MSC:
90C15 Stochastic programming
62L20 Stochastic approximation
68Q25 Analysis of algorithms and problem complexity
90C26 Nonconvex programming, global optimization
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