Free Access
Issue
ESAIM: COCV
Volume 20, Number 2, April-June 2014
Page(s) 524 - 546
DOI https://doi.org/10.1051/cocv/2013074
Published online 27 March 2014
  1. K. Atkinson and W. Han, Theoretical Numerical Analysis: A Functional Analysis Framework. Springer (2009). [Google Scholar]
  2. M. Anitescu, P. Tseng and S.J. Wright, Elastic-mode algorithms for mathematical programs with equilibrium constraints: global convergence and stationarity properties. Math. Program 110 (2005) 337–371. [CrossRef] [Google Scholar]
  3. E. Bänsch, Local mesh refinement in 2 and 3 dimensions. IMPACT Comput. Sci. Engrg. 3 (1991) 181–198. [CrossRef] [MathSciNet] [Google Scholar]
  4. V. Barbu, Optimal Control of Variational Inequalities. Pitman, Boston, London, Melbourne (1984). [Google Scholar]
  5. D. Braess, C. Carstensen and R.H.W. Hoppe, Convergence analysis of a conforming adaptive finite element method for an obstacle problem. J. Numer. Math. 107 (2007) 455–471. [CrossRef] [Google Scholar]
  6. D. Braess, C. Carstensen and R.H.W. Hoppe, Error reduction in adaptive finite element approximations of elliptic obstacle problems. J. Comput. Math. 27 (2009) 148–169. [Google Scholar]
  7. R. Becker, H. Kapp and R. Rannacher, Adaptive finite element methods for optimal control of partial differential equations: Basic concept. SIAM J. Control Optim. (2000). [Google Scholar]
  8. W. Bangerth and R. Rannacher, Adaptive Finite Element Methods for Differential Equations. Birkhäuser Verlag, Basel (2003). [Google Scholar]
  9. D. Braess, A posteriori error estimators for obstacle problems – another look. Numer. Math. 101 (2005) 415–421. [CrossRef] [MathSciNet] [Google Scholar]
  10. O. Benedix and B. Vexler, A posteriori error estimation and adaptivity for elliptic optimal control problems with state constraints. Comput. Optim. Appl. 44 (2009) 3–25. [Google Scholar]
  11. I. Babuška, J. Whiteman and T. Strouboulis, Finite Elements: An Introduction to the Method and Error Estimation. Oxford University Press (2011). [Google Scholar]
  12. C. Carstensen, An adaptive mesh-refining algorithm allowing for an stable projection onto Courant finite element spaces. Constructive Approximation 20 (2004) 549–564. [CrossRef] [MathSciNet] [Google Scholar]
  13. M.C. Ferris and T.S. Munson, Interfaces to path 3.0: Design, implementation and usage. Comput. Optim. Appl. 12 207–227 (1999). [CrossRef] [Google Scholar]
  14. F. Facchinei and J.S. Pang. Finite-Dimensional Variational Inequalities and Complementarity Problems, in vol. 1 of Springer Ser. Oper. Research. Springer (2003). [Google Scholar]
  15. A. Günther and M. Hinze, A posteriori error control of a state constrained elliptic control problem. J. Numer. Math. 16 (2008) 307–322. [MathSciNet] [Google Scholar]
  16. M. Hintermüller and R.H.W. Hoppe, Goal-oriented adaptivity in control constrained optimal control of partial differential equations. SIAM J. Control Optim. 47 (2008) 1721–1743. [CrossRef] [MathSciNet] [Google Scholar]
  17. M. Hintermüller and R.H.W. Hoppe, Goal-oriented adaptivity in pointwise state constrained optimal control of partial differential equations. SIAM J. Control Optim. 48 (2010) 5468–5487. [CrossRef] [MathSciNet] [Google Scholar]
  18. M. Hintermüller and R.H.W. Hoppe, Goal-oriented mesh adaptivity for mixed control-state constrained elliptic optimal control problems, in vol. 15 of Appl. Numer. Partial Differ. Eq., edited by W. Fitzgibbon, Y.A. Kuznetsov, P. Neittaanmäki and J. Périaux. Comput. Methods Appl. Sci. Springer, Berlin-Heidelberg-New York (2010) 97–111. [Google Scholar]
  19. M. Hintermüller, M. Hinze and M.H. Tber, An adaptive finite-element Moreau-Yosida-based solver for a non-smooth CahnHilliard problem. Optim. Methods Software 26 (2011) 777–811. [Google Scholar]
  20. M. Hintermüller, K. Ito and K. Kunisch. The primal-dual active set strategy as a semismooth Newton method. SIAM J. Optim. 13 (2002) 865–888. [Google Scholar]
  21. M. Hintermüller and I. Kopacka. Mathematical programs with complementarity constraints in function space: C- and strong stationarity and a path-following algorithm. SIAM J. Optim. 20 (2009) 868–902. [CrossRef] [MathSciNet] [Google Scholar]
  22. M. Hintermüller and I. Kopacka, A smooth penalty approach and a nonlinear multigrid algorithm for elliptic MPECs. Comput. Optim. Appl. 50 (2011) 111–145. DOI: 10.1007/s10589-009-9307-9. [CrossRef] [Google Scholar]
  23. M. Hintermüller and T. Surowiec, A bundle-free implicit programming approach for a class of MPECs in function space. Preprint (2012). [Google Scholar]
  24. C. Johnson, Adaptive finite element methods for the obstacle problem. Math. Models Methods Appl. Sci. 2 (1992) 483–487. [CrossRef] [Google Scholar]
  25. D. Klatte and B. Kummer, Nonsmooth Equations in Optimization: Regularity, Calculus, Methods and Applications. Nonconvex Optim. Appl. Kluwer Academic (2002). [Google Scholar]
  26. D. Kinderlehrer and G. Stampacchia, An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980). [Google Scholar]
  27. K. Kunisch and D. Wachsmuth. Path-following for optimal control of stationary variational inequalities. Comput. Optim. Appl. 51 (2012) 1345–1373. [Google Scholar]
  28. Z.Q. Luo, J.S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press (1996). [Google Scholar]
  29. W. Liu and N. Yan, A posteriori error estimates for distributed convex optimal control problems. Advances Comput. Math. 15 (2001) 285–309. [Google Scholar]
  30. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation I: Basic Theory, vol. 330 of Grundlehren der mathematischen Wissenschaften. Springer (2006). [Google Scholar]
  31. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation II: Applications, vol. 331 of Grundlehren der mathematischen Wissenschaften. Springer (2006). [Google Scholar]
  32. F. Mignot and J.P. Puel. Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466–476. [CrossRef] [MathSciNet] [Google Scholar]
  33. P. Neittaanmäki, J. Sprekels and D. Tiba, Optimization of Elliptic Systems: Theory and Applications. Springer Monogr. Math. Springer (2006). [Google Scholar]
  34. R.H. Nochetto, K.G. Siebert and A. Veeser, Pointwise a posteriori error control for elliptic obstacle problems. Numer. Math. 95 (2003) 163–195. DOI: 10.1007/s00211-002-0411-3. [CrossRef] [MathSciNet] [Google Scholar]
  35. J.V. Outrata, M. Kočvara and J. Zowe, Nonsmooth Approach to Optimization Problems with Equilibrium Constraints: Theory, Applications, and Numerical Results, vol. 152 of Nonconvex Optim. Appl. Kluwer Academic Publishers (1998). [Google Scholar]
  36. D. Ralph. Global convergence of damped Newton’s method for nonsmooth equations via the path search. Math. Oper. Res. 19 (1994) 352–389. [CrossRef] [MathSciNet] [Google Scholar]
  37. S.I. Repin, A Posteriori Estimates for Partial Differential Equations. Radon Ser. Comput. Appl. Math. De Gruyter (2008). [Google Scholar]
  38. J.-F. Rodrigues, Obstacle Problems in Mathematical Physics. North-Holland, Amsterdam (1987). [Google Scholar]
  39. A. Rösch and D. Wachsmuth, A posteriori error estimates for optimal control problems with state and control constraints. Numer. Math. 120 (2012) 733–762. [CrossRef] [MathSciNet] [Google Scholar]
  40. H. Scheel and S. Scholtes, Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Research 25 (2000) 1–22. [Google Scholar]
  41. A. Veeser, Efficient and reliable a posteriori error estimators for elliptic obstacle problems. SIAM J. Numer. Anal. 39 (2001) 146–167. [CrossRef] [MathSciNet] [Google Scholar]
  42. R. Verfürth, A review of a posteriori error estimation and adaptive mesh-refinement techniques. Wiley-Teubner (1996). [Google Scholar]
  43. B. Vexler and W. Wollner, Adaptive finite elements for elliptic optimization problems with control constraints. SIAM J. Control Optim. 47 (2008) 509–534. [Google Scholar]

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