Abstract
Consider a linear program in which the entries of the coefficient matrix vary linearly with time. To study the behavior of optimal solutions as time goes to infinity, it is convenient to express the inverse of the basis matrix as a series expansion of powers of the time parameter. We show that an algorithm of Wilkinson (1982) for solving singular differential equations can be used to obtain such an expansion efficiently. The resolvent expansions of dynamic programming are a special case of this method.
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Lamond, B.F. A generalized inverse method for asymptotic linear programming. Mathematical Programming 43, 71–86 (1989). https://doi.org/10.1007/BF01582279
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DOI: https://doi.org/10.1007/BF01582279