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

J. C. Reyes () and C. Meyer ()
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J. C. Reyes: EPN Quito
C. Meyer: Technische Universität Dortmund

Journal of Optimization Theory and Applications, 2016, vol. 168, issue 2, No 1, 375-409

Abstract: 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.

Keywords: Variational inequalities; Optimality conditions; Mathematical programs with equilibrium constraints; 49K21; 90C33; 35R35; 49J40 (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1007/s10957-015-0748-2

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