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Stochastic Optimization MethodsStochastic Optimization Methods

Stochastic Optimization Methods: Stochastic Optimization Methods [Many concrete problems from engineering, economics, operations research, etc., can be formulated by an optimization problem of the type 1.1a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} \min f_{0}(a,x)& &{}\end{array}$$ \end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} \mbox{ s.t.}& & {}\\ & & {}\\ \end{array}$$ \end{document}1.1b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} f_{i}(a,x)& \leq & 0,i = 1,\ldots,m_{f}{}\end{array}$$ \end{document}1.1c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} g_{i}(a,x)& =& 0,i = 1,\ldots,m_{g}{}\end{array}$$ \end{document}1.1d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} x \in D_{0}.& &{}\end{array}$$ \end{document}] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Stochastic Optimization MethodsStochastic Optimization Methods

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References (109)

Publisher
Springer Berlin Heidelberg
Copyright
© Springer-Verlag Berlin Heidelberg 2015
ISBN
978-3-662-46213-3
Pages
1 –35
DOI
10.1007/978-3-662-46214-0_1
Publisher site
See Chapter on Publisher Site

Abstract

[Many concrete problems from engineering, economics, operations research, etc., can be formulated by an optimization problem of the type 1.1a\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} \min f_{0}(a,x)& &{}\end{array}$$ \end{document}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} \mbox{ s.t.}& & {}\\ & & {}\\ \end{array}$$ \end{document}1.1b\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} f_{i}(a,x)& \leq & 0,i = 1,\ldots,m_{f}{}\end{array}$$ \end{document}1.1c\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} g_{i}(a,x)& =& 0,i = 1,\ldots,m_{g}{}\end{array}$$ \end{document}1.1d\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document} $$\displaystyle\begin{array}{rcl} x \in D_{0}.& &{}\end{array}$$ \end{document}]

Published: Jan 30, 2015

Keywords: Limit State Function; Robust Optimal Design; Primary Cost; Production Planning Problem; Stochastic Uncertainty

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