## Numerical OptimizationNumerical 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

1 | |

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 |

637 | |

653 | |