Strong Stationarity Conditions for a Class of Optimization Problems Governed by Variational Inequalities of the Second Kind

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 problems and for problems in function spaces, under suitable assumptions on the active set. A characterization of Bouligand and strong stationary points is obtained thereafter. Finally, based on the obtained first-order information, a trust-region algorithm is proposed for the solution of the optimization problems.

Año de publicación:

2016

Keywords:

• Optimality conditions
• Mathematical programs with equilibrium constraints
• Variational inequalities

Fuente:

scopus

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