## Optimization by Vector Space MethodsEngineers must make decisions regarding the distribution of expensive resources in a manner that will be economically beneficial. This problem can be realistically formulated and logically analyzed with optimization theory. This book shows engineers how to use optimization theory to solve complex problems. Unifies the large field of optimization with a few geometric principles. Covers functional analysis with a minimum of mathematics. Contains problems that relate to the applications in the book. |

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### Contents

LINEAR SPACES | 11 |

2 | 17 |

HILBERT SPACE | 46 |

OTHER MINIMUM NORM PROBLEMS | 64 |

LEASTSQUARES ESTIMATION | 78 |

1 | 103 |

GEOMETRIC FORM OF THE HAHNBANACH | 129 |

LINEAR OPERATORS AND ADJOINTS | 143 |

ADJOINTS | 150 |

OPTIMIZATION IN HILBERT SPACE | 160 |

OPTIMIZATION OF FUNCTIONALS | 169 |

GLOBAL THEORY OF CONSTRAINED OPTIMIZATION | 213 |

LOCAL THEORY OF CONSTRAINED OPTIMIZATION | 239 |

5 | 253 |

ITERATIVE METHODS OF OPTIMIZATION | 271 |

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### Common terms and phrases

additional analysis applied approximation arbitrary assume Banach space chapter closed complete components cone conjugate consider consisting constraints contains continuous convergence convex convex set corresponding defined definition denoted derivatives determined direction discussed dual duality element equal equation equivalent estimate Example exists expressed Figure finding finite fixed follows Fréchet differentiable functional f geometric given hence Hilbert space hyperplane implies important independent inequality integral interior point Lagrange multiplier Lemma linear functional mapping matrix maximize measurements method minimizing minimum norm necessary normed space Note obtain operator optimal original orthogonal positive problem projection Proof properties Proposition prove random relation respect result satisfying scalar separating sequence Show simple solution solved sphere subset subspace Suppose technique theorem theory transformation unique variable vector space zero