Generalized derivatives of the optimal value of a linear program with respect to matrix coefficients

We present here a characterization of the Clarke subdifferential of the optimal value function of a linear program as a function of matrix coefficients. We generalize the result of Freund (1985) to the cases where derivatives may not be defined because of the existence of multiple primal or dual solutions. (c) 2020 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/)

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The article presents a characterization of the Clarke subdifferential of the optimal value function of a linear program in terms of matrix coefficients. It generalizes the result of Freund (1985) to situations where derivatives may not be defined due to the presence of multiple primal or dual solutions.