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An Infinite-Dimensional LP Duality Theorem

Department of Statistics, University of Kentucky, 817 Patterson Office Tower, Lexington, Kentucky 40506-0027
scalar{at}ms.uky.edu

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.

Key Words: Linear program; strictly positive; adjoint operator; algebraic dual; topological dual
History: Received: August 28, 2001; revision received: June 11, 2002;revision received: October 14, 2002;

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