Nonlinear Optimization

ISBN-10: 0691119155
ISBN-13: 9780691119151
Edition: 2006
List price: $105.00 Buy it from $72.93
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Description: Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various  More...

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Book details

List price: $105.00
Copyright year: 2006
Publisher: Princeton University Press
Publication date: 1/22/2006
Binding: Hardcover
Pages: 464
Size: 6.50" wide x 10.00" long x 1.50" tall
Weight: 1.738
Language: English

Optimization is one of the most important areas of modern applied mathematics, with applications in fields from engineering and economics to finance, statistics, management science, and medicine. While many books have addressed its various aspects,Nonlinear Optimizationis the first comprehensive treatment that will allow graduate students and researchers to understand its modern ideas, principles, and methods within a reasonable time, but without sacrificing mathematical precision. Andrzej Ruszczynski, a leading expert in the optimization of nonlinear stochastic systems, integrates the theory and the methods of nonlinear optimization in a unified, clear, and mathematically rigorous fashion, with detailed and easy-to-follow proofs illustrated by numerous examples and figures. The book covers convex analysis, the theory of optimality conditions, duality theory, and numerical methods for solving unconstrained and constrained optimization problems. It addresses not only classical material but also modern topics such as optimality conditions and numerical methods for problems involving nondifferentiable functions, semidefinite programming, metric regularity and stability theory of set-constrained systems, and sensitivity analysis of optimization problems. Based on a decade's worth of notes the author compiled in successfully teaching the subject, this book will help readers to understand the mathematical foundations of the modern theory and methods of nonlinear optimization and to analyze new problems, develop optimality theory for them, and choose or construct numerical solution methods. It is a must for anyone seriously interested in optimization.

Preface
Introduction
Theory
Elements of Convex Analysis
Convex Sets
Cones
Extreme Points
Convex Functions
Subdifferential Calculus
Conjugate Duality
Optimality Conditions
Unconstrained Minima of Differentiable Functions
Unconstrained Minima of Convex Functions
Tangent Cones
Optimality Conditions for Smooth Problems
Optimality Conditions for Convex Problems
Optimality Conditions for Smooth-Convex Problems
Second Order Optimality Conditions
Sensitivity
Lagrangian Duality
The Dual Problem
Duality Relations
Conic Programming
Decomposition
Convex Relaxation of Nonconvex Problems
The Optimal Value Function
The Augmented Lagrangian
Methods
Unconstrained Optimization of Differentiable Functions
Introduction to Iterative Algorithms
Line Search
The Method of Steepest Descent
Newton's Method
The Conjugate Gradient Method
Quasi-Newton Methods
Trust Region Methods
Nongradient Methods
Constrained Optimization of Differentiable Functions
Feasible Point Methods
Penalty Methods
The Basic Dual Method
The Augmented Lagrangian Method
Newton's Method
Barrier Methods
Nondifferentiable Optimization
The Subgradient Method
The Cutting Plane Method
The Proximal Point Method
The Bundle Method
The Trust Region Method
Constrained Problems
Composite Optimization
Nonconvex Constraints[406
Stability of Set-Constrained Systems
Linear-Conic Systems
Set-Constrained Linear Systems
Set-Constrained Nonlinear Systems
Further Reading
Bibliography
Index

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