Paper Title:

Generalizing Polyhedra to Infinite Dimension

Author(s):

Paolo d'Alessandro

Department of Mathematics, Third University of Rome,
Lgo S.L. Murialdo 1, 00146 Rome, Italy.

dalex@mat.uniroma3.it.

URL: http://www.mat.uniroma3.it/users/dalex/dalex.html.

Abstract:

This paper generalizes polyhedra to infinite dimensional Hilbert spaces as countable intersections of closed semispaces. Highlights are the structure theory that shows that a polyhedron is the sum of compact set (in a suitable topology) plus a closed pointed cone plus a closed subspace, giving the internal representation of polyhedra. In the final part the dual range space technique is extended to the solution of infinite dimensional LP problems.

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