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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

We prove a novel optimality condition in terms of Bouligand generalizeddifferentials for a local minimizer of optimal control problems governed by anonsmooth semilinear elliptic partial differential equation with bothdistributed and boundary unilateral pointwise control constraints, in which thenonlinear coefficient in the state equation is not differentiable at one point.  Therefore, the Bouligand subdifferential of this nonsmooth coefficient inevery point consists of one or two elements that will be used to construct thetwo associated Bouligand generalized derivatives of the control-to-stateoperator in any admissible control.  We also establish the optimality conditions in the form of multiplierexistence. There, in addition to the existence of the adjoint state and of thenonnegative multipliers associated with the pointwise constraints as usual,other nonnegative multipliers exist and correspond to the nondifferentiabilityof the control-to-state mapping.  The latter type of optimality conditions shall be applied to the optimalcontrol problems without distributed and boundary pointwise constraints toderive the so-called \emph{strong} stationarity conditions, where the sign ofthe associated adjoint state does not vary on the level set of thecorresponding optimal state at the value of nondifferentiability.

Optimality conditions in terms of Bouligand generalized differentials  for a nonsmooth semilinear elliptic optimal control problem with distributed  and boundary control pointwise constraints