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Introduction to the Theory of Nonlinear Optimization /

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This book serves as an introductory text to optimization theory in normed spaces. Topics of this book are existence results, various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, and the investiga...

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Bibliographic Details
Main Author: Jahn, Johannes
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 1994.
Subjects:
Mathematics.
System theory.
Mathematical optimization.
Engineering mathematics.
Operations research.
Electronic books.
Online Access:Connect to the full text of this electronic book
Table of Contents:
  • Introduction and Problem Formulation
  • Existence Theorems for Minimal Points: Problem Formulation
  • Existence Theorems
  • Set of Minimal Points
  • Application to Approximation Problems
  • Application to Optimal Control Problems
  • Generalized Derivatives: Directional Derivative
  • Gâteaux and Fréchet Derivatives
  • Subdifferential
  • Quasidifferential
  • Clarke Derivative
  • Tangent Cones: Definition and Properties
  • Optimality Conditions
  • A Lyusternik Theorem
  • Generalized Lagrange Multiplier Rule: Problem Formulation
  • Necessary Optimality Conditions
  • Sufficient Optimality Conditions
  • Application to Optimal Control Problems
  • Duality: Problem Formulation
  • Duality Theorems
  • Saddle Point Theorems
  • Linear Problems
  • Application to Approximation Problems
  • Direct Treatment of Special Optimization Problems: Linear Quadratic Optimal Control Problems
  • Time Minimal Control Problems
  • Appendices: Weak Convergence
  • Reflexity of Banach Spaces
  • Hahn-Banach Theorem
  • Partially Ordered Linear Spaces.