# Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities

Karl Kunisch; Daniel Wachsmuth

ESAIM: Control, Optimisation and Calculus of Variations (2012)

- Volume: 18, Issue: 2, page 520-547
- ISSN: 1292-8119

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topKunisch, Karl, and Wachsmuth, Daniel. "Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities." ESAIM: Control, Optimisation and Calculus of Variations 18.2 (2012): 520-547. <http://eudml.org/doc/276369>.

@article{Kunisch2012,

abstract = {In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems as well. It is further shown that these conditions are also sufficient for
superlinear convergence of the semi-smooth Newton algorithm to be well-defined and
superlinearly convergent when applied to the first order optimality system associated with
the regularized problems. },

author = {Kunisch, Karl, Wachsmuth, Daniel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Variational inequalities; optimal control; sufficient optimality conditions; semi-smooth Newton method; variational inequalities},

language = {eng},

month = {7},

number = {2},

pages = {520-547},

publisher = {EDP Sciences},

title = {Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities},

url = {http://eudml.org/doc/276369},

volume = {18},

year = {2012},

}

TY - JOUR

AU - Kunisch, Karl

AU - Wachsmuth, Daniel

TI - Sufficient optimality conditions and semi-smooth newton methods for optimal control of stationary variational inequalities

JO - ESAIM: Control, Optimisation and Calculus of Variations

DA - 2012/7//

PB - EDP Sciences

VL - 18

IS - 2

SP - 520

EP - 547

AB - In this paper sufficient second order optimality conditions for optimal control problems
subject to stationary variational inequalities of obstacle type are derived. Since
optimality conditions for such problems always involve measures as Lagrange multipliers,
which impede the use of efficient Newton type methods, a family of regularized problems is
introduced. Second order sufficient optimality conditions are derived for the regularized
problems as well. It is further shown that these conditions are also sufficient for
superlinear convergence of the semi-smooth Newton algorithm to be well-defined and
superlinearly convergent when applied to the first order optimality system associated with
the regularized problems.

LA - eng

KW - Variational inequalities; optimal control; sufficient optimality conditions; semi-smooth Newton method; variational inequalities

UR - http://eudml.org/doc/276369

ER -

## References

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