Fréchet differentiability of Lipschitz functions via a variational principle

Joram Lindenstrauss; David Preiss; Jaroslav Tišer

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The question of Lipschitz continuity of solutions to parameterized variational inequalities with perturbed constraint sets is considered. Under the sole Lipschitz continuity assumption on data, a Lipschitz continuity result is proved which, in particular, holds for variational inequalities modeling evolutionary network equilibrium problems. Moreover, in view of real-life applications, a long-term memory is introduced and the corresponding variational inequality model is discussed. ...