Appl Math Optim 41:343–364 (2000)
2000 Springer-Verlag New York Inc.
Optimal Control of Elliptic Variational Inequalities
and K. Kunisch
Department of Mathematics, North Carolina State University,
Raleigh, NC 27695, USA
Institut f¨ur Mathematik, Karl-Franzens-Universit¨at Graz,
A-8010 Graz, Austria
Communicated by J. Stoer
Abstract. Optimality systems for optimal control problems governed by elliptic
variational inequalities are derived. Existence of appropriately deﬁned Lagrange
multipliers is proved. A primal–dual active set method is proposed to solve the
optimality systems numerically. Examples with and without lack of strict comple-
mentarity are included.
Key Words. Optimal control, Variational inequalities, Augmented Lagrangians,
Lagrange multipliers, Active set methods, Strict complementarity.
AMS Classiﬁcation. 49J24, 49J40, 49K24, 90C30.
In this paper we continue our line of investigation of augmented Lagrangian techniques
as an efﬁcient tool for both analysis and numerical treatment of optimization problems
The research of Kazufumi Ito was supported in part by AFSOR under Contracts F-49620-95-1-0437
and F-49620-95-1-0447, and that of Karl Kunisch was supported in part by the Fonds zur F¨orderung der
wissenschaftlichen Forschung, SFB “Optimization and Control.”