## 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. Drawing on their experiences in teaching, research, and consulting, the authors have produced a textbook that will be of interest to students and practitioners alike. Each chapter begins with the basic concepts and builds up gradually to the best techniques currently available. 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. Above all, 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. MMOR Mathematical Methods of Operations Research, 2001: "The book looks very suitable to be used in an graduate-level course in optimization for students in mathematics, operations research, engineering, and others. Moreover, it seems to be very helpful to do some self-studies in optimization, to complete own knowledge and can be a source of new ideas.... I recommend this excellent book to everyone who is interested in optimization problems." |

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### Vsebina

Introduction | 1 |

Fundamentals of Unconstrained Optimization | 11 |

Line Search Methods | 35 |

TrustRegion Methods | 65 |

Conjugate Gradient Methods | 101 |

Practical Newton Methods | 135 |

Notes and References | 162 |

Notes and References | 189 |

Theory of Constrained Optimization | 315 |

The Simplex Method | 363 |

InteriorPoint Methods | 395 |

Fundamentals of Algorithms for Nonlinear Cons trained Optimization | 420 |

Penalty Barrier and Augmented Lagrangian Methods | 491 |

Sequential Quadratic Programming | 529 |

Elements of Analysis Geometry Topology | 577 |

Elements of Linear Algebra | 593 |

Notes and References | 219 |

Nonlinear LeastSquares Problems | 251 |

Nonlinear Equations | 277 |

611 | |

625 | |

### Pogosti izrazi in povedi

algorithm approach approximate solution automatic differentiation BFGS BFGS method bound Cauchy point Chapter choose columns components compute conjugate gradient method constrained optimization curvature decrease defined denote derivatives descent direction described diagonal differentiable direction pk discussion eigenvalues elements equality constraints equality-constrained evaluation example feasible point feasible region feasible sequence Figure global convergence Hessian approximation implementation inequality constraints interior-point Jacobian KKT conditions L-BFGS Lagrange multiplier Lagrangian Lemma LICQ line search linear programming Lipschitz continuous matrix merit function minimizer Newton step Newton's method node nonsingular nonzero norm objective function obtain optimization problems parameter partially separable positive definite primal-dual proof properties quadratic programming quasi-Newton methods require result satisfies scalar search direction second-order solving SQP methods steepest descent step length strategy subproblem subspace sufficiently superlinear Suppose symmetric techniques term Theorem trust-region unconstrained variables vector Wolfe conditions xk+i zero