Introduction to the Theory of Optimization in Euclidean Space

Samia Challal (Autor)

Buch | Softcover

336 Seiten

2021
Chapman & Hall/CRC (Verlag)
978-1-032-17661-1 (ISBN)

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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

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.

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.

Erscheinungsdatum	01.10.2021
Reihe/Serie	Chapman & Hall/CRC Series in Operations Research
Sprache	englisch
Maße	156 x 234 mm
Gewicht	462 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Allgemeines / Lexika
	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
ISBN-10	1-032-17661-X / 103217661X
ISBN-13	978-1-032-17661-1 / 9781032176611
Zustand	Neuware