## Numerical OptimizationPresents a comprehensive & up-to-date description of the most effective methods in continuous optimization. It responds to the growing interest in optimization in engineering, science & business by focusing on the methods that are best suited to practical problems. Drawing on their experiences in teaching, research & consulting, the authors have produced a textbook that will be of interest to students & practitioners alike. Each chapter begins with the basic concepts & builds up gradually to the best techniques currently available. |

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### Contents

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 | |

### Common terms and phrases

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