## 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 |

Some practical issues | 49 |

Integer programming | 59 |

Nonlinear Programming | 67 |

Introduction | 111 |

Variational Problems and Dynamic Programming | 137 |

justification | 153 |

Variational problems under integral and pointwise restrictions 159 6 Summary of restrictions for variational problems | 168 |

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### Common terms and phrases

algorithms associated Assume Ax=b Chapter columns computations conditions of optimality constant convex function corresponding cost functional derivative descent direction determine the optimal differentiable duality dynamic programming E-L equation endpoint conditions entering variable Example feasible vectors Figure find the optimal formulation function f g(xk given global minimum Hamiltonian inequalities initial integral constraints integral curves integrand interval KKT conditions leaving variable linear system matrix Maximize maximum Minimize cx Minimize f(x multipliers NLPP 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 primal problem Minimize quadratic readers respect 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