Stochastic Optimization Methods

  • Kurt Marti

Table of contents

About this book

Introduction

Optimization problems arising in practice involve random parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, deterministic substitute problems are needed. Based on the distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Deterministic and stochastic approximation methods and their analytical properties are provided: Taylor expansion, regression and response surface methods, probability inequalities, First Order Reliability Methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation methods, differentiation of probability and mean value functions. Convergence results of the resulting iterative solution procedures are given.

Keywords

Optimization Problems Response surface methodology Stochastic Approximation calculus control optimization stochastic optimization uncertainty

Authors and affiliations

  • Kurt Marti
    • 1
  1. 1.Aero-Space Engineering and TechnologyFederal Armed Forces University MunichNeubiberg/MunichGermany

Bibliographic information

  • DOI https://doi.org/10.1007/b138181
  • Copyright Information Springer Berlin · Heidelberg 2005
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-540-22272-9
  • Online ISBN 978-3-540-26848-2
  • About this book