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

Abstract

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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.

How to cite

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Kunisch, 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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