The Australian Journal of Mathematical Analysis and Applications

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ISSN 1449-5910  


Paper Information

Paper Title:

Generalizing Polyhedra to Infinite Dimension


Paolo d'Alessandro

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



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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