Numerical Optimization

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Springer Science & Business Media, Dec 11, 2006 - Mathematics - 664 pages
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Numerical Optimization presents a comprehensive and up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science, and business by focusing on the methods that are best suited to practical problems.

For this new edition the book has been thoroughly updated throughout. There are new chapters on nonlinear interior methods and derivative-free methods for optimization, both of which are used widely in practice and the focus of much current research. Because of the emphasis on practical methods, as well as the extensive illustrations and exercises, the book is accessible to a wide audience. It can be used as a graduate text in engineering, operations research, mathematics, computer science, and business. It also serves as a handbook for researchers and practitioners in the field. The authors have strived to produce a text that is pleasant to read, informative, and rigorous - one that reveals both the beautiful nature of the discipline and its practical side.

There is a selected solutions manual for instructors for the new edition.

 

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Contents

Introduction
1
Fundamentals of Unconstrained Optimization
10
Line Search Methods
30
TrustRegion Methods
66
Conjugate Gradient Methods
101
QuasiNewton Methods
135
LargeScale Unconstrained Optimization
164
Calculating Derivatives
193
A Background Material
598
Norms
600
Subspaces
602
Eigenvalues Eigenvectors and the SingularValue Decomposition
603
DeterminantandTrace
605
CholeskyLUQR
606
SymmetricIndefiniteFactorization
610
ShermanMorrisonWoodburyFormula
612

DerivativeFree Optimization
220
LeastSquares Problems
245
Nonlinear Equations
270
Theory of Constrained Optimization
304
The Simplex Method
355
Penalty and Augmented Lagrangian Methods
497
NotesandReferences
526
Sequential Quadratic Programming
529
InteriorPoint Methods for Nonlinear Programming
563
DescriptionofaTrustRegionInteriorPointMethod
582
ThePrimalLogBarrierMethod
583
GlobalConvergenceProperties
587
ModifiedLineSearchMethods
589
SuperlinearConvergence
591
PerspectivesandSoftware
592
NotesandReferences
593
Exercises
594
InterlacingEigenvalueTheorem
613
ConditioningandStability
616
ElementsofAnalysisGeometryTopology
617
RatesofConvergence
619
Topology of the Euclidean Space IRn
620
Convex Sets in IRn
621
ContinuityandLimits
623
Derivatives
625
DirectionalDerivatives
628
MeanValueTheorem
629
ImplicitFunctionTheorem
630
OrderNotation
631
RootFindingforScalarEquations
633
B A Regularization Procedure
635
References
637
Index
653
Copyright

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