Applied Mathematics and Optimization

, Volume 41, Issue 3, pp 343–364

Optimal Control of Elliptic Variational Inequalities

  • K. Ito
  • K. Kunisch

DOI: 10.1007/s002459911017

Cite this article as:
Ito, K. & Kunisch, K. Appl Math Optim (2000) 41: 343. doi:10.1007/s002459911017


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 complementarity are included.

Key words. Optimal control, Variational inequalities, Augmented Lagrangians, Lagrange multipliers, Active set methods, Strict complementarity. AMS Classification. 49J24, 49J40, 49K24, 90C30.

Copyright information

© 2000 Springer-Verlag New York Inc.

Authors and Affiliations

  • K. Ito
    • 1
  • K. Kunisch
    • 2
  1. 1.Department of Mathematics, North Carolina State University, Raleigh, NC 27695, USA US
  2. 2.Institut für Mathematik, Karl-Franzens-Universität Graz, A-8010 Graz, Austria AT