Introduction to the Theory of Nonlinear Optimization

This book provides an introduction to optimization theory in normed spaces, covering existence results, differentiability notions, optimality conditions, contingent cone, Lagrange multiplier rule, duality theory, extended semidefinite optimization, and linear quadratic and time minimal control problems. It has been extensively revised and includes a new chapter on discrete-continuous optimization.

Format: Paperback / softback
Length: 323 pages
Publication date: 03 July 2021
Publisher: Springer Nature Switzerland AG

This comprehensive textbook provides an in-depth introduction to optimization theory in normed spaces, covering a wide range of topics. It begins by exploring existence results, which establish the conditions for the existence of solutions to optimization problems. The book then delves into various differentiability notions, including the concept of differentiability and the theory of partial derivatives. It also discusses optimality conditions, which are necessary for determining the optimal solutions to optimization problems.

The contingent cone, a generalization of the Lagrange multiplier rule, is introduced as a tool for analyzing optimization problems. Duality theory, which provides insights into the relationship between optimization problems and linear programming, is also discussed. Extended semidefinite optimization is introduced as a technique for solving complex optimization problems with semidefinite constraints.

Furthermore, the book explores linear quadratic and time minimal control problems, which are important in various fields such as engineering and economics. Each chapter is accompanied by exercises to help the reader consolidate their understanding of the material.

The fourth edition of this textbook has undergone extensive revision, and a new chapter on discrete-continuous optimization has been added. This edition is designed to meet the needs of both undergraduate and graduate students in mathematics, engineering, and applied sciences.

Overall, this textbook is a valuable resource for anyone interested in learning about optimization theory in normed spaces. Its comprehensive coverage, clear explanations, and extensive exercises make it an ideal text for both self-study and classroom use.

Weight: 516g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030427627
Edition number: 4th ed. 2020