Abstract
We derive conditions for the local uniqueness of solutions of nonlinear complementarity problems (NCP). We then prove the existence, continuity, and directional differentiability of a locally unique parametric solution of the parametric NCP under stronger assumptions. In the absence of degeneracy this parametric solution is also shown to be continuously differentiable.
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Kyparisis, J. Uniqueness and differentiability of solutions of parametric nonlinear complementarity problems. Mathematical Programming 36, 105–113 (1986). https://doi.org/10.1007/BF02591993
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DOI: https://doi.org/10.1007/BF02591993