Introduction to the Theory of Optimization in Euclidean Space

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.

"The textbook is relatively compact and written in a lecture note style that would be suitable for either a course or an independent study. Each mathematical theorem and its proof are complemented by examples and exercises that are mostly concrete and computational.[. . .] This book distinguishes itself among undergraduate optimization books by organically picking up where multivariable calculus leaves off, with regards to both topic selection and level of rigor and abstraction."—MAA 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."—Professor Salim Aissa Salah Messaoudi, University of Sharjah, UAE"This book, part of the CRC Series on Operations Research, is designed for undergraduate courses in operations research and mathematics. It starts at a fairly basic level, with open and closed sets, functions of more than one variable, surfaces in three dimensions, partial differentiation. The book is well produced. [. . .] It is worth consideration as a text for appropriate courses"—Mathematical Gazette

• 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.