This paper generalizes polyhedra to infinite dimensional separable Hilbert spaces as countable intersections of closed semispaces. We show that a polyhedron is the sum of convex proper subset, which is compact in the product topology, plus a closed pointed cone plus a closed subspace. In the final part the dual range space technique is extended to solve infinite dimensional LP problems.
D'Alessandro, P. (2010). Generalizing polyhedra to infinite dimensions. AUSTRALIAN JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 7(2), 1-22.
Generalizing polyhedra to infinite dimensions
D'ALESSANDRO, Paolo
2010-01-01
Abstract
This paper generalizes polyhedra to infinite dimensional separable Hilbert spaces as countable intersections of closed semispaces. We show that a polyhedron is the sum of convex proper subset, which is compact in the product topology, plus a closed pointed cone plus a closed subspace. In the final part the dual range space technique is extended to solve infinite dimensional LP problems.File in questo prodotto:
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