## Introduction to OptimizationThis undergraduate textbook introduces students of science and engineering to the fascinating field of optimization. It is a unique book that brings together the subfields of mathematical programming, variational calculus, and optimal control, thus giving students an overall view of all aspects of optimization in a single reference. As a primer on optimization, its main goal is to provide a succinct and accessible introduction to linear programming, nonlinear programming, numerical optimization algorithms, variational problems, dynamic programming, and optimal control. Prerequisites have been kept to a minimum, although a basic knowledge of calculus, linear algebra, and differential equations is assumed. |

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### Contents

Linear Programming | 23 |

The simplex method | 30 |

Duality | 42 |

Some practical issues | 49 |

Integer programming | 59 |

Nonlinear Programming | 67 |

KarushKuhnTucker optimality conditions | 79 |

Convexity | 86 |

justification | 153 |

Variational problems under integral and pointwise restrictions | 160 |

Summary of restrictions for variational problems | 168 |

Bellmans equation | 178 |

Some basic ideas on the numerical approximation | 185 |

Optimal Control | 195 |

Pontryagins principle | 204 |

Another format | 224 |

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### Common terms and phrases

algorithms associated Assume Chapter columns computations conditions of optimality conjugate directions conjugate gradient conjugate gradient method constant convex function corresponding cost functional derivative descent direction deta determine the optimal Differential Equations duality dynamic programming E-L equation endpoint conditions entering variable Example feasible vectors Figure find the optimal formulation function f given global minimum Hamiltonian inequalities infimum initial integral constraints integral curves integrand interval KKT conditions leaving variable linear system mathematical matrix Maximize maximum Minimize f(x multipliers necessary conditions negative component NLPP node nonlinear programming nonnegative Notice numerical approximation objective function obtain optimal control problem optimal solution optimal strategy optimality conditions optimization problem parameter particular point of minimum positive possible primal quadratic readers restrictions satisfy search direction simplex method situation stopping criterion strictly convex subintervals subject to g(x subproblem surface of revolution Theorem transversality condition typical vanish variational problems Vf(x