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Foundations of Optimization (Springer Series in Operations Research and Financial Enginee)

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Foundations of Optimization (Springer Series in Operations Research and Financial Enginee) Cover

 

Synopses & Reviews

Publisher Comments:

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.

Synopsis:

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.

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 semidefinite 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.

Table of Contents

Calculus in Vector Spaces.- Unconstrained Optimization.- Convex Analysis.- Theory of Convex Polyhedra.- Some Basic Optimization Algorithms.- Theory of Lagrange Multipliers.- Semi-infinite Programming.- Duality Theory and Convex Programming.- References.- Index.

Product Details

ISBN:
9780387344317
Author:
Guler, Osman
Publisher:
Springer
Subject:
Linear Programming
Subject:
Applied
Subject:
Operations Research
Subject:
Mathematics-Computer
Subject:
Ekeland s epsilon-variational principle
Subject:
Newton s method
Subject:
Conjugate Gradient Method
Subject:
convex polyhedra
Subject:
Convexity
Subject:
Duality
Subject:
Mathematical programming
Subject:
nonlinear analysis
Subject:
Optimality conditions
Subject:
OPTIMIZATION
Subject:
semi-infinite programming
Subject:
steepest-descent method
Subject:
Calculus of Variations and Optimal Control; Optimization
Subject:
Operations Research, Management Science
Subject:
APPLICATIONS OF MATHEMATICS
Subject:
Business Writing
Copyright:
Edition Description:
2010
Series:
Graduate Texts in Mathematics
Series Volume:
258
Publication Date:
20100825
Binding:
HARDCOVER
Language:
English
Pages:
460
Dimensions:
235 x 155 mm 1810 gr

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Foundations of Optimization (Springer Series in Operations Research and Financial Enginee) New Hardcover
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Product details 460 pages Springer - English 9780387344317 Reviews:
"Synopsis" by , 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.
"Synopsis" by , 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 semidefinite 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.
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