- J.Z. Ben-Asher, E.M. Cliff and J.A. Burns, Computational methods for the minimum effort problem with applications to spacecraft rotational maneuvers, in IEEE Conf. on Control and Applications (1989) 472–478.
- C. Clason, K. Ito and K. Kunisch, Minimal invasion : An optimal L∞ state constraint problem. ESAIM : M2AN 45 (2010) 505–522. [CrossRef] [EDP Sciences]
- I. Ekeland and R. Témam, Convex analysis and variational problems, Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (1999).
- D. Gilbarg and N.S. Trudinger, Elliptic Partial Differential Equations of Second Order, Classics in Mathematics. Springer-Verlag, Berlin (2001). Reprint of the 1998 edition.
- T. Grund and A. Rösch, Optimal control of a linear elliptic equation with a supremum norm functional. Optim. Methods Softw. 15 (2001) 299–329. [CrossRef] [MathSciNet] [PubMed]
- M. Gugat and G. Leugering, L∞-norm minimal control of the wave equation : On the weakness of the bang-bang principle. ESAIM Control Optim. Calc. Var. 14 (2008) 254–283. [CrossRef] [EDP Sciences] [MathSciNet]
- K. Ito and K. Kunisch, Lagrange Multiplier Approach to Variational Problems and Applications, Advances in Design and Control. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA 15 (2008).
- K. Ito and K. Kunisch, Minimal effort problems and their treatment by semismooth newton methods. SIAM J. Control Optim. 49 (2011) 2083–2100. [CrossRef] [MathSciNet]
- O.A. Ladyzhenskaya and N.N. Ural’tseva, Linear and quasilinear elliptic equations. Translated from the Russian by Scripta Technica, Inc. Translation, edited by L. Ehrenpreis, Academic Press, New York (1968).
- L.W. Neustadt, Minimum effort control systems. SIAM J. Control Ser. A 1 (1962) 16–31.
- U. Prüfert and A. Schiela, The minimization of a maximum-norm functional subject to an elliptic PDE and state constraints. Z. Angew. Math. Mech. 89 (2009) 536–551. [CrossRef] [MathSciNet]
- A. Schiela, A simplified approach to semismooth Newton methods in function space. SIAM J. Optim. 19 (2008) 1417–1432. [CrossRef]
- Z. Sun and J. Zeng, A damped semismooth Newton method for mixed linear complementarity problems. Optim. Methods Softw. 26 (2010) 187–205. [CrossRef] [MathSciNet] [PubMed]
- G.M. Troianiello, Elliptic Differential Equations and Obstacle Problems. The University Series in Mathematics, Plenum Press, New York (1987).
- F. Tröltzsch, Optimal Control of Partial Differential Equations : Theory, Methods and Applications. American Mathematical Society, Providence (2010). Translated from the German by Jürgen Sprekels.
- E. Zuazua, Controllability and observability of partial differential equations : some results and open problems, in Handbook of differential equations : evolutionary equations. Handb. Differ. Equ., Elsevier, North, Holland, Amsterdam III (2007) 527–621.
Volume 46, Number 4, July-August 2012
|Page(s)||911 - 927|
|Published online||03 February 2012|