Implicit B-Differentiability in Generalized Equations.
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WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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Generalized equations are mathematical models for nonlinear equilibrium problems in areas such as economics, transportation, etc. In such models, it is desirable to know how the solution of the model will change when the problem data change. When such a change is too hard to compute, a convenient approximation method may yield and answer that is good enough, particularly for small changes. This paper develops such an approximation. The author has previously proved an implicit-function theorem for regular solutions of generalized equations. Here he shows that when the underlying set for the generalized equation is polyhedral, as it is in many applications, then the implicit function has a Bouligand derivative defined by a formula generalizing that of the usual implicit-function theorem. This extends recent results on directional differentiability obtained by Kyparisis and others.
- Numerical Mathematics