Free access
Issue
ESAIM: M2AN
Volume 35, Number 1, January/February 2001
Page(s) 129 - 152
DOI http://dx.doi.org/10.1051/m2an:2001109
Published online 15 April 2002
  1. V. Barbu, Optimal Control of Variational Inequalities. Res. Notes Math., Pitman, 100 (1984).
  2. B. Bayada and M. El Aalaoui Talibi, Control by the coefficients in a variational inequality: the inverse elastohydrodynamic lubrication problem. Report no. 173, I.N.S.A. Lyon (1994).
  3. A. Bensoussan, J.L. Lions and G. Papanicolaou, Asymptotic Analysis for Periodic Structures, North-Holland, Amsterdam (1978).
  4. M. Bergounioux, Optimal control problems governed by abstract elliptic variational inequalities with state constraints. SIAM J. Control Optim. 36 (1998) 273-289. [CrossRef] [MathSciNet]
  5. M. Bergounioux and H. Dietrich, Optimal control problems governed by obstacle type variational inequalities: a dual regularization penalization approach. J. Convex Anal. 5 (1998) 329-351. [MathSciNet]
  6. M. Bergounioux, K. Ito and K. Kunisch, Primal-dual strategy for constrained optimal control problems. SIAM J. Control Optim. 37 (1999) 1176-1194. [CrossRef] [MathSciNet]
  7. M. Bergounioux and F. Mignot, Optimal control of obstacle problems: existence of Lagrange multipliers. ESAIM: COCV 5 (2000) 45-70. [CrossRef] [EDP Sciences]
  8. A. Bermudez and C. Saguez, Optimality conditions for optimal control problems of variational inequalities, in: Control problems for systems described by partial differential equations and applications. I. Lasiecka and R. Triggiani Eds., Lect. Notes Control and Information Sciences, Springer, Berlin (1987).
  9. G. Capriz and G. Cimatti, Free boundary problems in the theory of hydrodynamic lubrication: a survey, in: Free Boundary Problems: Theory and Applications, Vol. II, A. Fasano and M. Primicerio Eds., Res. Notes Math., Pitman, 79 (1983).
  10. G. Cimatti, On a problem of the theory of lubrication governed by a variational inequality. Appl. Math. Optim. 3 (1977) 227-242. [CrossRef]
  11. F. Clarke, Optimization and Nonsmooth Analysis. Wiley-Interscience, New York (1983).
  12. J. Dennis and R. Schnabel, Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Series in Computational Mathematics, Prentice-Hall, Englewood Cliffs, New Jersey (1983).
  13. F. Facchinei, A. Fischer and C. Kanzow, A semismooth Newton method for variational inequalities: the case of box constraints, in Complementarity and Variational Problems, State of the Art, M. Ferris and J. Pang Eds., SIAM, Philadelphia (1997).
  14. F. Facchinei, H. Jiang and L. Qi, A smoothing method for mathematical programs with equilibrium constraints. Math. Prog. 85 (1999) 107-134. [CrossRef]
  15. J. Guo, A variational inequality associated with a lubrication problem, IMA Preprint Series, no. 530 (1989).
  16. B. Hu, A quasi-variational inequality arising in elastohydrodynamics. SIAM J. Math. Anal. 21 (1990) 18-36. [CrossRef] [MathSciNet]
  17. K. Ito and K. Kunisch, On the injectivity and linearization of the coefficient-to-solution mapping for elliptic boundary value problems. J. Math. Anal. Appl. 188 (1994) 1040-1066. [CrossRef] [MathSciNet]
  18. K. Ito and K. Kunisch, Optimal control of elliptic variational inequalities. Appl. Math. Optim. 41 (2000) 343-364. [CrossRef] [MathSciNet]
  19. W. Liu and J. Rubio, Optimality conditions for strongly monotone variational inequalities. Appl. Math. Optim. 27 (1993) 291-312. [CrossRef] [MathSciNet]
  20. Z. Luo, J. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press, New York (1996).
  21. Z. Luo and P. Tseng, A new class of merit functions for the nonlinear complementarity problem, in Complementarity and Variational Problems, State of the Art, M. Ferris and J. Pang Eds., SIAM, Philadelphia (1997).
  22. F. Mignot and J.P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466-476. [CrossRef] [MathSciNet]

Recommended for you