Gerd Wachsmuth - From resolvents to generalized equations and quasi-variational inequalities: existence and differentiability

jnsao:8537 - Journal of Nonsmooth Analysis and Optimization, January 10, 2022, Volume 3 - https://doi.org/10.46298/jnsao-2022-8537
From resolvents to generalized equations and quasi-variational inequalities: existence and differentiability

Authors: Gerd Wachsmuth

We consider a generalized equation governed by a strongly monotone and Lipschitz single-valued mapping and a maximally monotone set-valued mapping in a Hilbert space. We are interested in the sensitivity of solutions w.r.t. perturbations of both mappings. We demonstrate that the directional differentiability of the solution map can be verified by using the directional differentiability of the single-valued operator and of the resolvent of the set-valued mapping. The result is applied to quasi-generalized equations in which we have an additional dependence of the solution within the set-valued part of the equation.


Volume: Volume 3
Section: Original research articles
Published on: January 10, 2022
Accepted on: January 7, 2022
Submitted on: September 30, 2021
Keywords: Mathematics - Optimization and Control,Mathematics - Functional Analysis,49J53, 47J22, 49J50


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