Introduction to the Theory of Optimization in Euclidean Space
1st Edition
Published on 11. November 2019
334 pages
978-0-429-51173-8 (ISBN)
Description
Introduction to the Theory of Optimization in Euclidean Space is intended to provide students with a robust introduction to optimization in Euclidean space, demonstrating the theoretical aspects of the subject whilst also providing clear proofs and applications.
Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations.
Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses.
Features
Rigorous and practical, offering proofs and applications of theorems
Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers
Introduces complex principles in a clear, illustrative fashion
Students are taken progressively through the development of the proofs, where they have the occasion to practice tools of differentiation (Chain rule, Taylor formula) for functions of several variables in abstract situations.
Throughout this book, students will learn the necessity of referring to important results established in advanced Algebra and Analysis courses.
Features
Rigorous and practical, offering proofs and applications of theorems
Suitable as a textbook for advanced undergraduate students on mathematics or economics courses, or as reference for graduate-level readers
Introduces complex principles in a clear, illustrative fashion
Reviews / Votes
"This book fills in the gap between the advanced, theoretical books on abstract Hilbert spaces, and the more practical books intended for Engineers, where theorems lack proofs. The author presents many theorems, along with their proofs, in a simple way and provides many examples and graphical illustrations to allow students grasp the material in an easy and quick way."-Professor Salim Aissa Salah Messaoudi, University of Sharjah, UAE
More details
Series
Edition
1. Auflage
Language
English
Place of publication
London
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Illustrations
38 Tables, black and white; 126 Line drawings, black and white
ISBN-13
978-0-429-51173-8 (9780429511738)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
09/2021
1st Edition
Chapman & Hall/CRC
€75.10
Shipment within 10-20 days
Book
11/2019
1st Edition
Chapman & Hall/CRC
€172.60
Shipment within 15-20 days
Person
Samia Challal is an assistant professor of Mathematics at Glendon College, the bilingual campus of York University. Her research interests include, homogenization, optimization, free boundary problems, partial differential equations, and problems arising from mechanics.
Content
1. Introduction. 1.1 Formulation of some optimization problems. 1.2 Particular subsets of Rn. 1.3 Functions of several variables. 2. Unconstrained Optimization. 2.1 Necessary condition. 2.2 Classification of local extreme points. 2.3 Convexity/concavity and global extreme points. 3. Constrained Optimization - Equality constraints. 3.1 Tangent plane. 3.2 Necessary condition for local extreme points-Equality constraints. 3.3 Classification of local extreme points-Equality constraints. 3.4 Global extreme points-Equality constraints. 4. Constrained Optimization - Inequality constraints. 4.1 Cone of feasible directions. 4.2 Necessary condition for local extreme points/Inequality constraints. 4.3 Classification of local extreme points-Inequality constraints. 4.4 Global extreme points-Inequality constraints. 4.5 Dependence on parameters.
