Foundations of Optimization
Seiten
2012
|
2010 ed.
Springer-Verlag New York Inc.
978-1-4614-2647-9 (ISBN)
Springer-Verlag New York Inc.
978-1-4614-2647-9 (ISBN)
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.
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.
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.
Differential Calculus.- Unconstrained Optimization.- Variational Principles.- Convex Analysis.- Structure of Convex Sets and Functions.- Separation of Convex Sets.- Convex Polyhedra.- Linear Programming.- Nonlinear Programming.- Structured Optimization Problems.- Duality Theory and Convex Programming.- Semi-infinite Programming.- Topics in Convexity.- Three Basic Optimization Algorithms.
| Reihe/Serie | Graduate Texts in Mathematics ; 258 |
|---|---|
| Zusatzinfo | XVIII, 442 p. |
| Verlagsort | New York, NY |
| Sprache | englisch |
| Maße | 155 x 235 mm |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Mathematik / Informatik ► Mathematik ► Finanz- / Wirtschaftsmathematik | |
| Wirtschaft ► Betriebswirtschaft / Management | |
| Schlagworte | conjugate-gradient method • Convexity • convex polyhedra • Duality • Ekeland's epsilon-variational principle • Linear Programming • Mathematical Programming • Newton's method • Nonlinear analysis • Optimality conditions • Optimization • semi-infinite programming • steepest-descent method |
| ISBN-10 | 1-4614-2647-2 / 1461426472 |
| ISBN-13 | 978-1-4614-2647-9 / 9781461426479 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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