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Issue
ESAIM: COCV
Volume 27, 2021
Article Number 45
Number of page(s) 31
DOI https://doi.org/10.1051/cocv/2021022
Published online 11 May 2021
  1. R.A. Adams and J.J.F. Fournier, Sobolev Spaces. Elsevier Science (2003). [Google Scholar]
  2. J.T. Betts and S.L. Campbell, Discretize then Optimize. Mathematics in Industry: Challenges and Frontiers A Process View: Practice and Theory. Edited by D.R. Ferguson and T.J. Peters. SIAM Publications, Philadelphia (2005). [Google Scholar]
  3. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer (2000). [CrossRef] [Google Scholar]
  4. A. Borzi, Multigrid methods for parabolic distributed optimal control problems. J. Comput. Appl. Math. 157 (2003) 365–382. [Google Scholar]
  5. J.C. Butcher, Numerical Methods for Ordinary Differential Equations. Wiley & Sons, Chichester (2016). [Google Scholar]
  6. E. Casas, Second order analysis for bang-bang control problems of PDEs. SIAM J. Control Optim. 50 (2012) 2355–2372. [CrossRef] [MathSciNet] [Google Scholar]
  7. E. Casas and M. Mateos, Critical cones for sufficient second order conditions in PDE constrained optimization. SIAM J. Optim. 30 (2020) 585–603. [CrossRef] [Google Scholar]
  8. C. Christof and G. Wachsmuth, On second-order optimality conditions for optimal control problems governed by the obstacle problem. Optimization 2020 (2020) 1–41. [Google Scholar]
  9. F.H. Clarke, Optimization and Nonsmooth Analysis. Wiley (1983). [Google Scholar]
  10. C. Clason, Y. Deng, P. Mehlitz and U. Prüfert, Optimal control problems with control complementarity constraints: existence results, optimality conditions, and a penalty method. Optim. Methods Softw. 35 (2020) 142–170. [Google Scholar]
  11. C. Clason, K. Ito and K. Kunisch, A convex analysis approach to optimal controls with switching structure for partial differential equations. ESAIM: COCV 22 (2016) 581–609. [CrossRef] [EDP Sciences] [Google Scholar]
  12. C. Clason, A. Rund and K. Kunisch, Nonconvex penalization of switching control of partial differential equations. Syst. Control Lett. 106 (2017) 1–8. [Google Scholar]
  13. C. Clason, A. Rund, K. Kunisch and R.C. Barnard, A convex penalty for switching control of partial differential equations. Syst. Control Lett. 89 (2016) 66–73. [Google Scholar]
  14. Y. Deng, P. Mehlitz and U. Prüfert, Optimal control in first-order Sobolev spaces with inequality constraints. Comput. Optim. Appl. 72 (2019) 797–826. [Google Scholar]
  15. E.D. Dolan and J.J. Moré, Benchmarking optimization software with performance profiles. Math. Program. 91 (2002) 201–213. [Google Scholar]
  16. J.C. Dunn, On Second order sufficient conditions for structured nonlinear programs in infinite-dimensional function spaces. In Math. Program. with Data Perturbations. Edited by A.V. Fiacco. Marcel Dekker Inc., New York (1998) 83–108. [Google Scholar]
  17. A. Fischer, A special Newton-type optimization method. Optimization 24 (1992) 269–284. [CrossRef] [MathSciNet] [Google Scholar]
  18. A. Galántai, Properties and construction of NCP functions. Comput. Optim. Appl. 52 (2012) 805–824. [Google Scholar]
  19. C. Geiger and C. Kanzow, Theorie und Numerik restringierter Optimierungsaufgaben. Springer, Berlin (2002). [Google Scholar]
  20. L. Guo and J.J. Ye, Necessary optimality conditions for optimal control problems with equilibrium constraints. SIAM J. Control Optim. 54 (2016) 2710–2733. [Google Scholar]
  21. F. Harder and G. Wachsmuth, Comparison of optimality systems for the optimal control of the obstacle problem. GAMM-Mitteilungen 40 (2018) 312–338. [Google Scholar]
  22. F. Harder and G. Wachsmuth, The limiting normal cone of a complementarity set in Sobolev spaces. Optimization 67 (2018) 1579–1603. [Google Scholar]
  23. M. Hintermüller, B.S. Mordukhovich and T.M. Surowiec, Several approaches for the derivation of stationarity conditions for elliptic MPECs with upper-level control constraints. Math. Program. 146 (2014) 555–582. [Google Scholar]
  24. M. Hintermüller and T.M. Surowiec, First-order optimality conditions for elliptic mathematical programs with equilibrium constraints via variational analysis. SIAM J. Optim. 21 (2011) 1561–1593. [Google Scholar]
  25. M. Hintermüller and T.M. Surowiec, On the directional differentiability of the solution mapping for a class of variational inequalities of the second kind. Set-Valued Variat. Anal. 26 (2017) 631–642. [Google Scholar]
  26. M. Hintermüller and M. Ulbrich, A mesh-independence result for semismooth Newton methods. Math. Program. 101 (2004) 151–184. [Google Scholar]
  27. T. Hoheisel, C. Kanzow and A. Schwartz, Theoretical and numerical comparison of relaxation methods for mathematical programs with complementarity constraints. Math. Program. 137 (2013) 257–288. [Google Scholar]
  28. X.M. Hu and D. Ralph, Convergence of a penalty method for mathematical programs with complementarity constraints. J. Optim. Theory Appl. 123 (2004) 365–390. [Google Scholar]
  29. X.X. Huang, X.Q. Yang and D.L. Zhu, A sequential smooth penalization approach to mathematical programs with complementarity constraints. Numer. Funct. Anal. Optim. 27 (2006) 71–98. [Google Scholar]
  30. C. Kanzow and A. Schwartz, Mathematical programs with equilibrium constraints: enhanced Fritz–John-conditions, new constraint qualifications, and improved exact penalty results. SIAM J. Optim. 20 (2010) 2730–2753. [Google Scholar]
  31. C. Kanzow, N. Yamashita and M. Fukushima, New NCP-functions and their properties. J. Optim. Theory Appl. 94 (1997) 115–135. [Google Scholar]
  32. K. Kunisch and D. Wachsmuth, Sufficient optimality conditions and semi-smooth Newton methods for optimal control of stationary variational inequalities. ESAIM: COCV 18 (2012) 520–547. [CrossRef] [EDP Sciences] [Google Scholar]
  33. S. Leyffer, G. López-Calva and J. Nocedal, Interior methods for mathematical programs with complementarity constraints. SIAM J. Optim. 17 (2006) 52–77. [Google Scholar]
  34. G. Liu, J. Ye and J. Zhu, Partial exact penalty for mathematical programs with equilibrium constraints. Set-Valued Anal. 16 (2008) 785. [Google Scholar]
  35. Z.-Q. Luo, J.-S. Pang and D. Ralph, Mathematical Programs with Equilibrium Constraints. Cambridge University Press (1996). [Google Scholar]
  36. Z.-Q. Luo, J.-S. Pang, D. Ralph and S.-Q. Wu, Exact penalization and stationarity conditions of mathematical programs with equilibrium constraints. Math. Program. 75 (1996) 19–76. [Google Scholar]
  37. H. Maurer and J. Zowe, First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems. Math. Program. 16 (1979) 98–110. [Google Scholar]
  38. P. Mehlitz and G. Wachsmuth, The limiting normal cone to pointwise defined sets in Lebesgue spaces. Set-Valued Variat. Anal. 26 (2018) 449–467. [Google Scholar]
  39. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation. Springer-Verlag (2006). [Google Scholar]
  40. I. Neitzel, U. Prüfert and T. Slawig, Strategies for time-dependent PDE control with inequality constraints using an integrated modeling and simulation environment. Numerical Algor. 50 (2009) 241–269. [Google Scholar]
  41. J.-S. Pang and D.E. Stewart, Differential variational inequalities. Math. Program. A 113 (2008) 345–424. [Google Scholar]
  42. L. Petzold, J.B. Rosen, P.E. Gill, L.O. Jay and K. Park, Numerical optimal control of parabolic PDEs using DASOPT. In Large-Scale Optimization with Applications. Edited by L.T. Biegler, T.F. Coleman, A.R. Conn, and F.N. Santosa. Vol. 93 of The IMA Volumes in Mathematics and its Applications. Springer, New York (1997). [Google Scholar]
  43. U. Prüfert, OOPDE: An object oriented toolbox for finite elements in Matlab. TU Bergakademie Freiberg (2015). [Google Scholar]
  44. U. Prüfert, Solving optimal PDE control problems. Optimality conditions, algorithms and model reduction. Habilitation thesis, TU Bergakademie Freiberg (2016). [Google Scholar]
  45. D. Ralph and S.J. Wright, Some properties of regularization and penalization schemes for MPECs. Optim. Methods Softw. 19 (2004) 527–556. [Google Scholar]
  46. S. Scheeland S. Scholtes, Mathematical programs with complementarity constraints: stationarity, optimality, and sensitivity. Math. Oper. Res. 25 (2000) 1–22. [Google Scholar]
  47. A. Schiela and D. Wachsmuth, Convergence analysis of smoothing methods for optimal control of stationary variational inequalities with control constraints. ESAIM: M2AN 47 (2013) 771–787. [CrossRef] [EDP Sciences] [Google Scholar]
  48. S. Scholtes and M. Stöhr, Exact penalization of mathematical programs with equilibrium constraints. SIAM J. Control Optim. 37 (1999) 617–652. [Google Scholar]
  49. D. Sun and L. Qi, On NCP-functions. Comput. Optim. Appl. 13 (1999) 201–220. [Google Scholar]
  50. F. Tröltzsch, Optimal Control of Partial Differential Equations: Theory, Methods and Applications. American Mathematical Society (2010). [Google Scholar]
  51. M. Ulbrich, Semismooth Newton methods for operator equations in function spaces. SIAM J. Optim. 13 (2002) 805–841. [Google Scholar]
  52. M. Ulbrich, Semismooth Newton Methods for Variational Inequalities and Constrained Optimization Problems in Function Spaces. MOS-SIAM (2011). [CrossRef] [Google Scholar]
  53. G. Wachsmuth, Mathematical programs with complementarity constraints in Banach spaces. J. Optim. Theory Appl. 166 (2015) 480–507. [Google Scholar]
  54. G. Wachsmuth, Towards M-stationarity for optimal control of the obstacle problem with control constraints. SIAM J. Control Optim. 54 (2016) 964–986. [Google Scholar]
  55. G. Wachsmuth, Elliptic quasi-variational inequalities under a smallness assumption: uniqueness, differential stability and optimal control. Calc. Variat. Partial Differ. Equ. 59 (2020). [Google Scholar]
  56. J. Wloka, Partielle Differentialgleichungen: Sobolevräume und Randwertaufgaben. Teubner (1982). [Google Scholar]
  57. J.J. Ye, Necessary and sufficient optimality conditions for mathematical programs with equilibrium constraints. J. Math. Anal. Appl. 307 (2005) 350–369. [Google Scholar]
  58. F. Yılmaz and B. Karasözen, An all-at-once approach for the optimal control of the unsteady Burgers equation. J. Comput. Appl. Math. 259 (2014) 771–779. [Google Scholar]

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