## Lecture Notes in Mathematics, Issue 257 |

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### Contents

Preliminaries 1 | ix |

SI Notation 1 | x |

3 The Separation Theorems | 4 |

Copyright | |

29 other sections not shown

### Common terms and phrases

Amer apply assume Banach space best approximation bounded characterization Chebyshev subspace compact condition constraints continuous functions convergence convex cone convex function convex program convex set convex subset Corollary defined Definition dual space Duality E-property E-space element epi f equation example Exercise existence ext U(X extreme point f e Conv finite dimensional follows formula given Haar subspace hence Hilbert space hyperplane implies inequality inner product space inverse Krein-Milman Theorem Lagrange multiplier Lagrange multiplier vector Lemma Let f linear functionals linear space linear subspace mapping Math metric projections n-dimensional open set optimization ordinary convex program polynomial problem Proof proximinal pseudoinverse real lcs reflexive reflexive space resp scalars sequence smooth subdifferential Suppose Theorem theory uniformly rotund unique x-xQ