Newton - Type Methods for Stochastic
نویسنده
چکیده
Stochastic programming is concerned with practical procedures for decision-making under uncertainty , by modelling uncertainties and risks associated with decisions in a form suitable for optimization. The eld is developing rapidly with contributions from many disciplines such as operations research, probability and statistics, and economics. A stochastic linear program with recourse can equivalently be formulated as a convex programming problem. The problem is often large-scale as the objective function involves an expectation, either over a discrete set of scenarios or as a multidimensional integral. Moreover, the objective function is possibly nondiierentiable. This paper provides a brief overview of recent developments on smooth approximation techniques and Newton-type methods for solving two-stage stochastic linear programs with recourse, and parallel implementation of these methods. A simple numerical example is used to signal the potential of smoothing approaches.
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