Inverse Linear Program by Modifying the Right-Hand Side Vector under l1 Norm

Abstract

Inverse linear programming problem (ILPb) by modifying the right-hand vector is discussed in the paper. A mathematical model of (ILPb), which is an MPEC problem, is constructed based on duality theories, and then a necessary and sufficient condition of checking the feasibility of (ILPb) is provided. The inverse problem under $l_1$ norm is transformed into a problem under weighted sum-type Hamming distance with linear equality and inequality constraints. An optimal solution in the special case is also given when the dual constraint conditions are all equalities and the coefficient matrix is invertible. In this case, the system of linear equations has the only solution.