## The best approximation and optimization in locally convex spaces |

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### Contents

DUALITY IN VECTORIAL OPTIMIZATION PROGRAMS WITH | 79 |

Duality | 92 |

4 Existence Results for Efficient Points | 108 |

Copyright | |

1 other sections not shown

### Common terms and phrases

additive set functions APPROXIMATION IN LOCALLY Banach space best approximation best simultaneous approximation best vectorial approximation bounded p-variation bounded set chsu closed and supernormal compact contradiction convex cone convex set convex subset convex with respect Corollary countable additive set defined denote duality efficient points elements of best elements of G example family of seminorms following theorem function f g0eG H-locally Hausdorff locally convex Hence Hilbert space implies Lemma locally convex space locally convex topology MIN(A minimal element multifunction non-empty and convex non-empty set non-empty subset normed vector space obtain P-simultaneous polynomial function real linear space real numbers Remark saddle point seminorms which induces simultaneous proximinal simultaneous strictly convex spline functions supernormal cone taking into account TeL(X,Z Theorem Theorem 3.2 topological vector space topology induced vectorial conjugate vectorial optimization problems vectorial strictly convex vectorial subdifferentiable virtue of Theorem x0 by G x0eX xcD(f xeD(f yef(u