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Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems. (English) Zbl 0613.90066
It is shown that solutions of linear inequalities, linear programs and certain linear complementarity problems (e.g. those with P-matrices or Z- matrices but not semidefinite matrices) are Lipschitz continuous with respect to changes in the right-hand side data of the problem. Solutions of linear programs are not Lipschitz continuous with respect to the coefficients of the objective function. The Lipschitz constant given here is a generalization of the role played by the norm of the inverse of a nonsingular matrix in bounding the perturbation of the solution of a system of equations in terms of a right-hand side perturbation.
90C05Linear programming
90C33Complementarity and equilibrium problems; variational inequalities (finite dimensions)