On the Lipschitzian properties of polyhedral multifunctions |
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Authors: | M Seetharama Gowda Roman Sznajder |
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Institution: | (1) Department of Mathematics and Statistics, University of Maryland Baltimore County, 21228 Baltimore, MD, USA |
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Abstract: | In this paper, we show that for a polyhedral multifunctionF:R
n
→R
m
with convex range, the inverse functionF
−1
is locally lower Lipschitzian at every point of the range ofF (equivalently Lipschitzian on the range ofF) if and only if the functionF is open. As a consequence, we show that for a piecewise affine functionf:R
n
→R
n
,f is surjective andf
−1
is Lipschitzian if and only iff is coherently oriented. An application, via Robinson's normal map formulation, leads to the following result in the context
of affine variational inequalities: the solution mapping (as a function of the data vector) is nonempty-valued and Lipschitzian
on the entire space if and only if the solution mapping is single-valued. This extends a recent result of Murthy, Parthasarathy
and Sabatini, proved in the setting of linear complementarity problems.
Research supported by the National Science Foundation Grant CCR-9307685. |
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Keywords: | Polyhedral multifunction Lipschitzian Coherence Open Error bound Affine variational inequality |
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