An infinite-dimensional linear program duality theorem

An infinite-dimensional linear program duality theorem

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Article ID: iaor2004397
Country: United States
Volume: 28
Issue: 2
Start Page Number: 233
End Page Number: 245
Publication Date: May 2003
Journal: Mathematics of Operations Research
Authors:
Keywords: duality
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.

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