English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper we investigate the sensitivity analysis of parameterizednonlinear variational inequalities of second kind in a Hilbert space. Thechallenge of the present work is to take into account a perturbation on all thedata of the problem. This requires special adjustments in the definitions ofthe generalized first- and second-order differentiations of the involvedoperators and functions. Precisely, we extend the notions, introduced andthoroughly studied by R.T. Rockafellar, of twice epi-differentiability andproto-differentiability to the case of a parameterized lower semi-continuousconvex function and its subdifferential respectively. The link between thesetwo notions is tied to Attouch's theorem and to the new concept, introduced inthis paper, of convergent supporting hyperplanes. The previous tools allow usto derive an exact formula of the proto-derivative of the generalized proximityoperator associated to a parameterized variational inequality, and deduce thedifferentiability of the associated solution with respect to the parameter.Furthermore, the derivative is shown to be the solution of a new variationalinequality involving semi- and twice epi-derivatives of the data. Anapplication is given to parameterized convex optimization problems involvingthe sum of two convex functions (one of them being smooth). The case of smoothconvex optimization problems with inequality constraints is discussed indetails. This approach seems to be new in the literature and open severalperspectives towards theoretical and computational issues in nonlinearoptimization.

Sensitivity analysis of variational inequalities via twice epi-differentiability and proto-differentiability of the proximity operator