## An Introduction to OptimizationPraise for the Third Edition ". . . guides and leads the reader through the learning path . . . [e]xamples are stated very clearly and the results are presented with attention to detail." —MAA Reviews Fully updated to reflect new developments in the field, the Fourth Edition of Introduction to Optimization fills the need for accessible treatment of optimization theory and methods with an emphasis on engineering design. Basic definitions and notations are provided in addition to the related fundamental background for linear algebra, geometry, and calculus. This new edition explores the essential topics of unconstrained optimization problems, linear programming problems, and nonlinear constrained optimization. The authors also present an optimization perspective on global search methods and include discussions on genetic algorithms, particle swarm optimization, and the simulated annealing algorithm. Featuring an elementary introduction to artificial neural networks, convex optimization, and multi-objective optimization, the Fourth Edition also offers: - A new chapter on integer programming
- Expanded coverage of one-dimensional methods
- Updated and expanded sections on linear matrix inequalities
- Numerous new exercises at the end of each chapter
- MATLAB exercises and drill problems to reinforce the discussed theory and algorithms
- Numerous diagrams and figures that complement the written presentation of key concepts
- MATLAB M-files for implementation of the discussed theory and algorithms (available via the book's website)
Introduction to Optimization, Fourth Edition is an ideal textbook for courses on optimization theory and methods. In addition, the book is a useful reference for professionals in mathematics, operations research, electrical engineering, economics, statistics, and business. |

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### Contents

Transformations | |

Concepts from Geometry | |

Elements of Calculus | |

Basics of SetConstrained | |

OneDimensional Search Methods | |

Gradient Methods | |

Global Search Algorithms | |

Introduction to Linear Programming | |

Simplex Method | |

Duality | |

Nonsimplex Methods | |

Problems with Equality Constraints | |

Integer Linear Programming | |

Problems with Inequality Constraints | |

Newtons Method | |

Coniugate Direction Methods | |

uasiNewton Methods | |

Solving Linear Equations | |

Unconstrained Optimization and Neural | |

Convex Optimization Problems | |

Algorithms for Constrained Optimization | |

### Other editions - View all

An Introduction to Optimization Edwin K. P. Chong,Stanislaw H. Zak,Stanislaw H. Żak Limited preview - 2013 |

### Common terms and phrases

augmented matrix basic feasible solution basis canonical augmented matrix chromosomes columns components compute Consider the problem constrained optimization convex function convex set corresponding denoted derivative dual duality eigenvalues equation Example Exercise exists feasible point feasible set Figure FONC formula function f genetic algorithm given global minimizer gradient algorithm Hence Hessian Hessian matrix inequality constraint input integer iteration Karmarkar’s KKT condition Lagrange condition least-squares Lemma linear programming problem LP problem MATLAB maximize multiobjective multiobjective optimization neural network neuron Newton’s method norm notation Note nullspace objective function objective function value obtain optimal solution optimization problem order of convergence orthogonal Pareto penalty function positive definite primal problem in standard problem minimize Proof pseudoinverse quadratic function rank satisfy secant method sequence Show simplex algorithm simplex method solve standard form steepest descent subspace Suppose symmetric tableau Theorem unconstrained update variables vector write