Stochastic linear programming. Models, theory, and computation
type: Item
instance of: scholarly article
title: Stochastic linear programming. Models, theory, and computation
zbMATH Open document ID: 1104.90033
author: P. Kall
author: J. Mayer
publication date: 2005-04-05T00:00:00Z
review text: This is a graduate text in optimisation whose main emphasis is in stochastic programming. The book is clearly written. The main stochastic models and programs are discussed at a high mathematical theoretical level while there are mentions to real life applications. The reader needs to have an adequate background of probability theory and optimisation. The authors are well known specialists with a large list of contributions in the theme. Stochastic Linear Programming (SLP) is emerging, as an indispensable tool for tackling the study of large sets of real life problems arising nowadays. The number of practical experiences, in its application to energy management, environmental, finances, production planning and other important areas, is growing. This is a good book for providing mathematicians, economists and engineers with an almost complete start up information for working in the field. I heartily welcome its publication. After an introduction the realm of the book begins, in Chapter 1, with the basics from linear programming, where the indispensable elements of algebra and geometry are presented. Later it goes to the simplex method, one of the most important tools in optimisation. We find there the basic concepts of decomposition (dual, nested, regularization) and on interior point methods. A discussion on nonlinear programming is also developed for guaranteeing the knowledge needed in the sequel. The second chapter is called single stage SLP-models. The authors introduce the related probability models and decision problems arising in recourse models. The different classes of SLP models are described and Lagrangian relaxation methods are discussed. Continuing with the convexity of the programs, the basic properties of the feasible sets, the considerations for the finite discrete distribution cases (the separate probability functions, the side stochastic right hand) as particular cases. The analysis of the behaviour of the mathematical models under normality, or wh…
reviewed by: Carlos Narciso Bouza Herrera
Mathematics Subject Classification ID: 90C15
Mathematics Subject Classification ID: 90C05
Mathematics Subject Classification ID: 90C25
Mathematics Subject Classification ID: 60E99
zbMATH DE Number: 2152357
zbMATH Keywords: stochastic linear programming
zbMATH Keywords: single stage SLP
zbMATH Keywords: probability constrained SLP
zbMATH Keywords: multistage SLP
zbMATH Keywords: algorithms
MaRDI profile type: Publication
published in: International Series in Operations Research & Management Science
description: scientific article; zbMATH DE number 2152357