## An Introduction to Unconstrained OptimisationIntegrating computer graphics and computer-based exercises with the text, An Introduction to Unconstrained Optimisation illustrates key methods with many examples and exercises using the computer. The book takes an elementary approach to this advanced topic, allowing readers to concentrate on learning and understanding the concepts of numerical optimization without unnecessary involvement in the intricacies of the subject. In addition, the modular approach of the software provides the opportunity to explore the algorithms used and to develop them further or try alternative approaches. Most of the algorithms are based upon a "hill-climbing" concept which, in two dimensions, is illustrated dynamically on the computer screen in the form of contour plots and search directions. The text is not specific to any particular microcomputer. Software is available for the BBC series of machines (40/80 track disc formats) and PC-compatible machines. The software is not available from your local bookstore, but is easily obtainable using the order form in the book. Keeping proofs and lists of methods to a minimum, the book is at a level suitable for a first course in numerical analysis, with a basic knowledge of calculus and vector algebra assumed. This book/software package will be of interest to professionals, teachers, and undergraduate students in mathematics, operational research, science, and engineering as well as economics and management courses that deal with quantitative methods. |

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### Contents

Searching for an optimum | 5 |

Line searches | 21 |

Direct search methods | 44 |

Gradient methods I | 61 |

Gradient methods II | 83 |

Optimisation in practice | 105 |

Bibliography | 119 |

### Common terms and phrases

arbitrary starting point BBC Basic bracketing interval Chapter components computed condition consider containing the minimum contour map contour plot convergence coordinate corresponds cubic search cycle defined determine the position direct search methods discussed display DSC algorithm E(dit efficient eigenvalues estimate Example Let Exercise F(xm F(xn Fibonacci search find the minimum function evaluations function F Gauss-Newton algorithm Gauss-Newton method global minimum global optimum golden section search gradient vector grid hessian matrix illustrates internal point iterations line searches local minimum locate maximum error menu minima minimisation minimum of F modified n-dimensional Newton's method number of function numerical optimisation obtained optimisation method orthogonal positive definite quadratic approximation quadratic function quadratic search Quasi-Newton Quasi-Newton methods saddle point satisfy screen search direction second derivatives Select some arbitrary sequence solution stationary points steepest descent algorithm step Stop sum of squares tion value of F variables zero

### Popular passages

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