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Stochastic First- and Zeroth-order Methods for Nonconvex Stochastic Programming

Saeed Ghadimi (sghadimi***at***ufl.edu)
Guanghui Lan (glan***at***ise.ufl.edu)

Abstract: In this paper, we introduce a new stochastic approximation (SA) type algorithm, namely the randomized stochastic gradient (RSG) method, for solving an important class of nonlinear (possibly nonconvex) stochastic programming (SP) problems. We establish the complexity of this method for computing an approximate stationary point of a nonlinear programming problem. We also show that this method possesses an optimal rate of convergence if the problem is convex. We discuss a variant of the algorithm which consists of applying a post-optimization phase to evaluate a short list of solutions generated by several independent runs of the RSG method, and show that such modification allows to improve significantly the large-deviation properties of the algorithm. These methods are then specialized for solving a class of simulation-based optimization problems in which only stochastic zeroth-order information is available.

Keywords: stochastic approximation, convex optimization, nonconvex optimization, stochastic programming, simulation-based optimization

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Category 2: Stochastic Programming

Category 3: Convex and Nonsmooth Optimization (Other )

Citation: Technical Report, Department of Industrial and Systems Engineering, University of Florida

Download: [PDF]

Entry Submitted: 06/09/2012
Entry Accepted: 06/09/2012
Entry Last Modified: 04/02/2013

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