Introduction to the Theory of Optimization in Euclidean Space

ISBN-13: 9781032176611 / Angielski / Miękka / 2021 / 336 str.

Samia Challal

Opis

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.

 

Spis treści

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.

O autorze

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.