Muutke küpsiste eelistusi

Introduction to the Theory of Optimization in Euclidean Space [Kõva köide]

  • Formaat: Hardback, 318 pages, kõrgus x laius: 234x156 mm, kaal: 780 g, 38 Tables, black and white; 126 Line drawings, black and white
  • Sari: Chapman & Hall/CRC Series in Operations Research
  • Ilmumisaeg: 14-Nov-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367195577
  • ISBN-13: 9780367195571
  • Formaat: Hardback, 318 pages, kõrgus x laius: 234x156 mm, kaal: 780 g, 38 Tables, black and white; 126 Line drawings, black and white
  • Sari: Chapman & Hall/CRC Series in Operations Research
  • Ilmumisaeg: 14-Nov-2019
  • Kirjastus: Chapman & Hall/CRC
  • ISBN-10: 0367195577
  • ISBN-13: 9780367195571
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

Arvustused

"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 "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

Preface ix
Acknowledgments xi
Symbol Description xiii
Author xv
1 Introduction
1(48)
1.1 Formulation of Some Optimization Problems
1(7)
1.2 Particular Subsets of Rn
8(12)
1.3 Functions of Several Variables
20(29)
2 Unconstrained Optimization
49(86)
2.1 Necessary Condition
49(22)
2.2 Classification of Local Extreme Points
71(22)
2.3 Convexity/Concavity and Global Extreme Points
93(24)
2.3.1 Convex/Concave Several Variable Functions
93(2)
2.3.2 Characterization of Convex/Concave C1 Functions
95(3)
2.3.3 Characterization of Convex/Concave C2 Functions
98(4)
2.3.4 Characterization of a Global Extreme Point
102(15)
2.4 Extreme Value Theorem
117(18)
3 Constrained Optimization-Equality Constraints
135(68)
3.1 Tangent Plane
137(14)
3.2 Necessary Condition for Local Extreme Points-Equality Constraints
151(16)
3.3 Classification of Local Extreme Points-Equality Constraints
167(20)
3.4 Global Extreme Points-Equality Constraints
187(16)
4 Constrained Optimization-Inequality Constraints
203(112)
4.1 Cone of Feasible Directions
204(16)
4.2 Necessary Condition for Local Extreme Points/Inequality Constraints
220(31)
4.3 Classification of Local Extreme Points-Inequality Constraints
251(20)
4.4 Global Extreme Points-Inequality Constraints
271(21)
4.5 Dependence on Parameters
292(23)
Bibliography 315(2)
Index 317
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.