Ebook: Introduction to the Theory of Nonlinear Optimization

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, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook 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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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, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook 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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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, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook 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.
Content:
Front Matter....Pages i-x
Introduction and Problem Formulation....Pages 1-5
Existence Theorems for Minimal Points....Pages 7-30
Generalized Derivatives....Pages 31-77
Tangent Cones....Pages 79-104
Generalized Lagrange Multiplier Rule....Pages 105-158
Duality....Pages 159-185
Application to Extended Semidefinite Optimization....Pages 187-211
Direct Treatment of Special Optimization Problems....Pages 213-240
Back Matter....Pages 241-292

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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, extended semidefinite optimization, and the investigation of linear quadratic and time minimal control problems. This textbook 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.
Content:
Front Matter....Pages i-x
Introduction and Problem Formulation....Pages 1-5
Existence Theorems for Minimal Points....Pages 7-30
Generalized Derivatives....Pages 31-77
Tangent Cones....Pages 79-104
Generalized Lagrange Multiplier Rule....Pages 105-158
Duality....Pages 159-185
Application to Extended Semidefinite Optimization....Pages 187-211
Direct Treatment of Special Optimization Problems....Pages 213-240
Back Matter....Pages 241-292
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