非線形最適化理論入門（第４版） Introduction to the Theory of Nonlinear Optimization （4TH）

Jahn, Johannes

Springer Nature Switzerland AG（2020/07発売）

• 製本 Hardcover:ハードカバー版／ページ数 323 p.
• 言語 ENG
• 商品コード 9783030427597

Full Description

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 4th 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.

Contents

Introduction and Problem Formulation.- Existence Theorems for Minimal Points.- Generalized Derivatives.- Tangent Cones.- Generalized Lagrange Multiplier Rule.- Duality.- Application to Extended Semidefinite Optimization.- Extension to Discrete-Continuous Problems.- Direct Treatment of Special Optimization Problems.