Nonlinear multiobjective optimization : a generalized homotopy approach /

Nonlinear multiobjective optimization : a generalized homotopy approach /

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Bibliographic Details
Author / Creator:Hillermeier, Claus, 1960-
Imprint:Boston : Birkhauser Verlag, 2000.
Description:135 p. : ill. ; 24 cm.
Language:English
Series:International series of numerical mathematics. v. 135
Subject:
Mathematical optimization.
Nonlinear programming.
Multiple criteria decision making.
Mathematical optimization.
Multiple criteria decision making.
Nonlinear programming.
Format: Print Book
URL for this record:http://pi.lib.uchicago.edu/1001/cat/bib/4376708
Hidden Bibliographic Details
ISBN:376436498X (alk. paper)
081766498X (alk. paper)
Notes:Includes bibliographical references and index.
Table of Contents:
  • 1. Introduction
  • 2. Vector Optimization in Industrial Applications
  • 2.1. The Design of a Combined-Cycle Power Plant
  • 2.2. The Optimal Operating Point of a Recovery-Boiler
  • 3. Principles and Methods of Vector Optimization
  • 3.1. The Concept of Pareto Optimality
  • 3.2. Survey of Methods
  • 3.3. A New Stochastic Method for Unconstrained Vector Optimization
  • 3.3.1. A Curve of Dominated Points
  • 3.3.2. Notions from Probability Theory
  • 3.3.3. A Special Stochastic Differential Equation
  • 3.3.4. A Stochastic Algorithm for Vector Optimization
  • 4. The Connection with Scalar-Valued Optimization
  • 4.1. The Karush-Kuhn-Tucker(KKT) Condition for Pareto Optimality
  • 4.2. Differential-Topological Notations
  • 4.3. The Geometrical Meaning of the Weight Vector
  • 4.4. Classification of Efficient Points
  • 5. The Manifold of Stationary Points
  • 5.1. Karush-Kuhn-Tucker Points as a Differentiable Manifold M
  • 5.2. Criteria for the Rank Condition
  • 5.2.1. A Necessary and Sufficient Criterion
  • 5.2.2. Interpretation in View of Optimization
  • 5.2.3. Variability of the Weight Vector
  • 5.3. A Special Class of Local Charts
  • 6. Homotype Strategies
  • 6.1. Method I: Local Exploration of M
  • 6.1.1. Method Principle
  • 6.1.2. Comparison with Classical Homotopy Method
  • 6.1.3. Homogeneous Discretization of the Efficient Set
  • 6.1.4. Numerical Algorithm
  • 6.2. Method II: Purposeful Change of the Weights
  • 6.2.1. Significance of the Weight Vector for the User
  • 6.2.2. Principle of the Procedure
  • 6.2.3. Numerical Algorithm
  • 7. Numerical Results
  • 7.1. Example 1 (academic)
  • 7.2. Example 2: Design of a Combined-Cycle Power Plant
  • 7.3. Example 3: The Optimal Operating Point of a Recovery-Boiler.

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