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arXiv · 1404.4787

Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the 2nd kind

Juan-Carlos De Los Reyes·Christian Meyer
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Abstract

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the solution map is studied. Directional differentiability is proved both for finite-dimensional and function space problems, under suitable assumptions on the active set. A characterization of B- and strong stationary optimal solutions is obtained thereafter. Finally, based on the obtained first-order information, a trust-region algorithm is proposed for the solution of the optimization problems.

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Juan-Carlos De Los Reyes, Christian Meyer. 2014-07-07. Strong stationarity conditions for a class of optimization problems governed by variational inequalities of the 2nd kind. https://arxiv.org/abs/1404.4787

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