Newton-type methods for stochastic programming

✍ Scribed by X Chen

• Publisher: Elsevier Science
• Year: 2000
• Tongue: English
• Weight: 765 KB
• Volume: 31
• Category: Article
• ISSN: 0895-7177
• DOI: 10.1016/s0895-7177(00)00075-3

✦ Synopsis

stochastic programming is concerned with practical procedures for decision making under uncertainty, by modelling uncertainties and risks associated with decision in a form suitable for optimization. The field 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 largescale as the objective function involves an expectation, either over a discrete set of scenarios or as a multi-dimensional integral. Moreover, the objective function is possibly nondifferentiable. This paper provides a brief overview of recent developments on smooth approximation techniques and Newton-type methods for solving twostage stochastic linear programs with recourse, and parallel implementation of these methods. A simple numerical example is used to signal the potential of smoothing approaches.