# Introduction to Theory of Optimization in Euclidean Space

## 1st Edition

CRC Press

336 pages

Hardback: 9780367195571
pub: 2019-10-24
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### Description

Introduction to 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
• Introduces complex principles in a clear, illustrative fashion

### Reviews

"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."

-Prof. Salim Aissa Salah Messaoudi, University of Sharjah, UAE

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

2.4 Extreme value theorem

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

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.