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Zbl 0613.90066
Mangasarian, O.L.; Shiau, T.-H.
Lipschitz continuity of solutions of linear inequalities, programs and complementarity problems. (English)
[J] SIAM J. Control Optimization 25, 583-595 (1987). ISSN 0363-0129; ISSN 1095-7138/e

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.

MSC 2000:: *90C05 Linear programming
90C33 Complementarity problems

Keywords: Lipschitz continuity; linear inequalities; linear complementarity; perturbation analysis

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