Introduction to the Theory of Nonlinear Optimization
By: by Johannes Jahn
Publisher: Springer Berlin Heidelberg
Published: 1994
Place of publication: Berlin, Heidelberg
Language: eng
Format: [electronic resource] /
Number of pages: 251
ISBN-13: 9783662029879; 9783662029855
Subjects: Mathematics; Mathematical optimization; Engineering mathematics; Operations research; Systems theory
Description: 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 investigation of linear quadratic and time minimal control problems. This book presents fundamentals with particular emphasis on the 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.
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Table of contents: title: Contents: Introduction and Problem Formulation; title: Existence Theorems for Minimal Points: Problem Formulation; title: Existence Theorems; title: Set of Minimal Points; title: Application to Approximation Problems; title: Application to Optimal Control Problems; title: Generalized Derivatives: Directional Derivative; title: Gâteaux and Fréchet Derivatives; title: Subdifferential; title: Quasidifferential; title: Clarke Derivative; title: Tangent Cones: Definition and Properties; title: Optimality Conditions; title: A Lyusternik Theorem; title: Generalized Lagrange Multiplier Rule: Problem Formulation; title: Necessary Optimality Conditions; title: Sufficient Optimality Conditions; title: Application to Optimal Control Problems; title: Duality: Problem Formulation; title: Duality Theorems; title: Saddle Point Theorems; title: Linear Problems; title: Application to Approximation Problems; title: Direct Treatment of Special Optimization Problems: Linear Quadratic Optimal Control Problems; title: Time Minimal Control Problems; title: Appendices: Weak Convergence; title: Reflexity of Banach Spaces; title: Hahn-Banach Theorem; title: Partially Ordered Linear Spaces.