## Introduction to Non-Linear OptimizationIn this textbook the author concentrates on presenting the main core of methods in non-linear optimization that have evolved over the past two decades. It is intended primarily for actual or potential practising optimizer who need to know how different methods work, how to select methods for the job in hand and how to use the chosen method. While the level of mathematical rigour is not very high, the book necessarily contains a considerable amount of mathematical argument and pre-supposes a knowledge such as would be attained by someone reaching the end of the second year of an undergraduate course in physical science, engineering or computational mathematics. The main emphasis is on linear algebra, and more advanced topics are discussed briefly where relevant in the text. The book will appeal to a range of students and research workers working on optimization problems in such fields as applied mathematics, computer science, engineering, business studies, economics and operations research. |

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### Contents

INTRODUCTION | 7 |

UNIVARIATE MINIMIZATION | 26 |

MULTIVARIATE MINIMIZATION | 56 |

Copyright | |

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active set Agfc approximation barrier function BFGS formula Bk+i Broyden's family compute condition number conjugate gradient methods deletion descent direction eigenvalues elements equality constraints exact linear search feasible point feasible region figure finite difference first-order Fk+i Fletcher function value Gauss-Newton method Gill and Murray Gill-Murray Golden Section search gradient evaluations gradient vector gtol Hessian matrix Hk+i inequality constraints input x0 interval reduction Lagrange multiplier estimates Lagrangian function Line Comments modified Newton method objective function obtained optimization passive constraints penalty function positive definite possible Projected Lagrangian methods quadratic function quadratic termination quasi-Newton methods rank-one rate of convergence saddle point satisfy scalar search vector second derivatives second-order solve stationary point steepest descent step strong minimum subspace sufficiently symmetric tangent hyperplane Taylor series techniques term unconstrained minimization xk+i zero