## Optimization: Insights and ApplicationsThis self-contained textbook is an informal introduction to optimization through the use of numerous illustrations and applications. The focus is on analytically solving optimization problems with a finite number of continuous variables. In addition, the authors provide introductions to classical and modern numerical methods of optimization and to dynamic optimization. The book's overarching point is that most problems may be solved by the direct application of the theorems of Fermat, Lagrange, and Weierstrass. The authors show how the intuition for each of the theoretical results can be supported by simple geometric figures. They include numerous applications through the use of varied classical and practical problems. Even experts may find some of these applications truly surprising. A basic mathematical knowledge is sufficient to understand the topics covered in this book. More advanced readers, even experts, will be surprised to see how all main results can be grounded on the Fermat-Lagrange theorem. The book can be used for courses on continuous optimization, from introductory to advanced, for any field for which optimization is relevant. |

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### Contents

3 | |

Two or More Variables without Constraints | 85 |

Equality Constraints | 135 |

Chapter 4 Inequality Constraints and Convexity | 199 |

Chapter 5 Second Order Conditions | 261 |

Chapter 6 Basic Algorithms | 273 |

Chapter 7 Advanced Algorithms | 325 |

Chapter 8 Economic Applications | 363 |

Vector and Matrix Calculus | 503 |

Appendix B On Real Analysis | 519 |

Appendix C The Weierstrass Theorem on Existence of Global Solutions | 537 |

Appendix D Crash Course on Problem Solving | 547 |

Geometrical Style | 553 |

Analytical Style | 561 |

Appendix G Conditions of Extremum from Fermat to Pontryagin | 583 |

Appendix H Solutions of Exercises of Chapters 14 | 601 |