Stability of solutions to parameterized nonlinear complementarity problems |
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Authors: | AB Levy |
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Institution: | (1) Department of Mathematics, Bowdoin College, Brunswick, ME 04011, USA, US |
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Abstract: | n such that x≥0, F(x,u)-v≥0 , and F(x,u)-v T·x=0 where these are vector inequalities. We characterize the local upper Lipschitz continuity of the (possibly set-valued)
solution mapping which assigns solutions x to each parameter pair (v,u). We also characterize when this solution mapping is
locally a single-valued Lipschitzian mapping (so solutions exist, are unique, and depend Lipschitz continuously on the parameters).
These characterizations are automatically sufficient conditions for the more general (and usual) case where v=0. Finally,
we study the differentiability properties of the solution mapping in both the single-valued and set-valued cases, in particular
obtaining a new characterization of B-differentiability in the single-valued case, along with a formula for the B-derivative.
Though these results cover a broad range of stability properties, they are all derived from similar fundamental principles
of variational analysis.
Received March 30, 1998 / Revised version received July 21, 1998
Published online January 20, 1999 |
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Keywords: | : parameterized nonlinear complementarity problems – solution stability – B-derivatives – Lipschitz continuity – local upper Lipschitz continuity |
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