Introduction to the Theory of Nonlinear Optimization
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Introduction to the Theory of Nonlinear Optimization

Introduction to the Theory of Nonlinear Optimization


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About the Book

This is an introductory text to optimization theory in normed spaces. It discusses existence results and various differentiability notions together with optimality conditions, the contingent cone, a generalization of the Lagrange multiplier rule, duality theory, and the investigation of linear quadratic and time minimal control problems. Particular emphasis is placed on application to problems in the calculus of variations, approximation and optimal control theory. The reader is expected to have a basic knowledge of linear functional analysis.

Table of Contents:
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 - Gteaux and Frchet 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.

Review :
From the reviews of the third edition: "Jahn 's textbook provides a thorough development of optimality conditions for optimization problems on function spaces. The book will be of interest to suitably prepared graduate students and researchers who are working on problems in optimal control theory. It may also be of interest to analysts who want to learn something about how functional analysis is used in the theory of optimization." (Brain Borchers, MathDL, April, 2007)"The third edition of this book has eight chapters . The book is written in a lucid style. It may be very useful to lecturers, students, and researchers." (Stanislaw Walczak, Zentralblatt MATH, Vol. 1115 (17), 2007)


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Product Details
  • ISBN-13: 9783540583202
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 216 mm
  • Returnable: N
  • Width: 138 mm
  • ISBN-10: 3540583203
  • Publisher Date: /10/1994
  • Binding: Hardback
  • Language: English
  • Weight: 495 gr


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