An infinite-dimensional LP duality theorem

Authors:
Stephen A. Clark
Affiliations:
Department of Statistics, University of Kentucky, 817 Patterson Office Tower, Lexington, Kentucky
Venue:
Mathematics of Operations Research
Year:
2003

Citing 3
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Abstract

This paper constructs an infinite-dimensional version of the Duality Theorem for a Linear Program (LP). The algebraic dual LP is replaced with a new program called the topological dual LP that closes the range of the adjoint operator. Under some mild nondegeneracy conditions involving strict positivity, the new Duality Theorem asserts that the optimal value of the primal LP equals the optimal value of the topological dual LP. Some applications to mathematical finance are also included.