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Stochastic Optimization Methods

  • Kurt┬áMarti

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Basic Stochastic Optimization Methods

  3. Differentiation Methods

  4. Deterministic Descent Directions

  5. Semi-Stochastic Approximation Methods

  6. Reliability Analysis of Structures/Systems

  7. Back Matter
    Pages 301-340

About this book

Introduction

Optimization problems arising in practice involve random model parameters. For the computation of robust optimal solutions, i.e., optimal solutions being insensitive with respect to random parameter variations, appropriate deterministic substitute problems are needed. Based on the probability distribution of the random data, and using decision theoretical concepts, optimization problems under stochastic uncertainty are converted into appropriate deterministic substitute problems. Due to the occurring probabilities and expectations, approximative solution techniques must be applied. Several deterministic and stochastic approximation methods are provided: Taylor expansion methods, regression and response surface methods (RSM), probability inequalities, multiple linearization of survival/failure domains, discretization methods, convex approximation/deterministic descent directions/efficient points, stochastic approximation and gradient procedures, differentiation formulas for probabilities and expectations.

Keywords

Operations Research Optimization Optimization Methods Optimization Problems Regression Response Surface Methodology Stochastic Approximation Stochastic Optimization calculus model

Authors and affiliations

  • Kurt┬áMarti
    • 1
  1. 1.Department of Aerospace Engineering and TechnologyUniversity Munich85577Germany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-79458-5
  • Copyright Information Springer Berlin Heidelberg 2008
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Business and Economics
  • Print ISBN 978-3-540-79457-8
  • Online ISBN 978-3-540-79458-5
  • Buy this book on publisher's site