Introduction to the Theory of Nonlinear Optimization

✍ Scribed by Johannes Jahn

• Publisher: Springer International Publishing;Springer
• Year: 2020
• Tongue: English
• Leaves: 325
• Edition: 4th ed.
• Category: Library

✦ Synopsis

This book offers an introduction to optimization theory in normed spaces. The topics covered include 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 an investigation of linear quadratic and time minimal control problems. The 4^th edition of this book has been extensively revised and a new chapter on discrete-continuous optimization has been added. This textbook focuses on the fundamentals, with particular emphasis on their application to problems in the calculus of variations, approximation and optimal control theory. The reader is assumed to have a basic grasp of linear functional analysis.

✦ Table of Contents

Front Matter ....Pages i-x
Introduction and Problem Formulation (Johannes Jahn)....Pages 1-7
Existence Theorems for Minimal Points (Johannes Jahn)....Pages 9-32
Generalized Derivatives (Johannes Jahn)....Pages 33-77
Tangent Cones (Johannes Jahn)....Pages 79-106
Generalized Lagrange Multiplier Rule (Johannes Jahn)....Pages 107-159
Duality (Johannes Jahn)....Pages 161-188
Application to Extended Semidefinite Optimization (Johannes Jahn)....Pages 189-211
Extension to Discrete-Continuous Problems (Johannes Jahn)....Pages 213-251
Direct Treatment of Special Optimization Problems (Johannes Jahn)....Pages 253-280
Back Matter ....Pages 281-323

✦ Subjects

Business and Management; Operations Research/Decision Theory; Optimization; Computational Intelligence