Foundations of Optimization

Osman Güler

ISBN 10: 1461426472 / ISBN 13: 9781461426479

Edité par Springer New York, Springer US, 2012

A propos de cet article

Druck auf Anfrage Neuware - Printed after ordering - The book gives a detailed and rigorous treatment of the theory of optimization (unconstrained optimization, nonlinear programming, semi-infinite programming, etc.) in finite-dimensional spaces. The fundamental results of convexity theory and the theory of duality in nonlinear programming and the theories of linear inequalities, convex polyhedra, and linear programming are covered in detail. Over two hundred, carefully selected exercises should help the students master the material of the book and give further insight. Some of the most basic results are proved in several independent ways in order to give flexibility to the instructor. A separate chapter gives extensive treatments of three of the most basic optimization algorithms (the steepest-descent method, Newton's method, the conjugate-gradient method). The first chapter of the book introduces the necessary differential calculus tools used in the book. Several chapters contain more advanced topics in optimization such as Ekeland's epsilon-variational principle, a deep and detailed study of separation properties of two or more convex sets in general vector spaces, Helly's theorem and its applications to optimization, etc. The book is suitable as a textbook for a first or second course in optimization at the graduate level. It is also suitable for self-study or as a reference book for advanced readers. The book grew out of author's experience in teaching a graduate level one-semester course a dozen times since 1993.Osman Guler is a Professor in the Department of Mathematics and Statistics at University of Maryland, Baltimore County. His research interests include mathematical programming, convex analysis, complexity of optimization problems, and operations research.

N° de réf. du vendeur 9781461426479

Détails bibliographiques

• Titre: Foundations of Optimization
• Éditeur: Springer New York, Springer US
• Date de parution: 2012
• Langue: anglais
• ISBN à 10 chiffres: 1461426472
• ISBN à 13 chiffres: 9781461426479
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 235 L x 155 H x 25 P (en millimètres) 235 millimètres de largeur par 155 millimètres de hauteur par 25 millimètres de profondeur
• Poids: 692 grammes

A propos de ce titre

Synopsis

This book is intended as a textbook to be used in a first graduate level course, and covers the fundamental principals of optimization in finite dimensions. It develops the necessary background material in multivariable calculus using coordinates as well as in a coordinate-free manner, so that the recent developments such as semi-definite programming can be dealt with ease. All the standard topics of mathematical programming, such as necessary and sufficient optimality conditions for optimality, convex analysis and duality, are covered in great detail, often from multiple points of view. A distinctive feature of this book is its set of worked-out examples and problems, including hundreds of well-chosen problems and important examples. It will be of benefit for graduate students and researchers in optimization, operations research.

Présentation de l'éditeur

This book covers the fundamental principles of optimization in finite dimensions. It develops the necessary material in multivariable calculus both with coordinates and coordinate-free, so recent developments such as semidefinite programming can be dealt with.