EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 32 (2026) ESAIM: COCV, 32 (2026) 40 References
Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 40
Number of page(s) 59
DOI https://doi.org/10.1051/cocv/2026022
Published online 06 May 2026
  1. W.W. Desch and J. Turi, The stop operator related to a convex polyhedron. J. Diff. Equ. 157 (1999) 329–347. [Google Scholar]
  2. P. Dupuis and H. Ishii, On Lipschitz continuity of the solution mapping to the Skorokhod problem, with applications. Stoch. Stoch. Rep. 35 (1991) 31–62. [Google Scholar]
  3. M.A. Krasnosel'skiiand A.V. Pokrovskii, Systems 'with Hysteresis, 1st edn. Springer, Berlin, Heidelberg (1989). [Google Scholar]
  4. P. Krejčí, Evolution variational inequalities and multidimensional hysteresis operators, in Nonlinear Differential Equations, vol. 404 of Research Notes in Mathematics, edited by P. Drábek, P. Krejčí and P. Takáč Chapman & Hall/CRC, London (1999) 47–110. [Google Scholar]
  5. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer Series in Operations Research. Springer, New York (2000). [Google Scholar]
  6. J.-J. Moreau, Problème d'evolution associé à un convexe mobile d'un espace hilbertien. C. R. Acad. Sci. Paris Sér. A-B 276 (1973) A791-A794. [Google Scholar]
  7. J.-J. Moreau, Evolution problem associated with a moving convex set in a Hilbert space. J. Diff. Equ. 26 (1977) 347–374. [Google Scholar]
  8. J.-J. Moreau, On unilateral constraints, friction and plasticity, in New Variational Techniques in Mathematical Physics, edited by G. Capriz and G. Stampacchia. Springer, Berlin, Heidelberg (2011) 171–322. [Google Scholar]
  9. P. Krejčí, Hysteresis, Convexity and Dissipation in Hyperbolic Equations, Vol. 8 of Mathematical Sciences and Applications. Gakkōtosho, Tokyo (1996). [Google Scholar]
  10. V. Acary, O. Bonnefon and B. Brogliato, Nonsmooth Modeling and Simulation for Switched Circuits. Lecture Notes in Electrical Engineering. Springer (2010). [Google Scholar]
  11. T.H. Cao, B.S. Mordukhovich, D. Nguyen and T. Nguyen, Applications of controlled sweeping processes to nonlinear crowd motion models with obstacles. IEEE Control Syst. Lett. 6 (2022) 740–745. [Google Scholar]
  12. A. Mielke and T. Roubíček, Rate-Independent Systems, vol. 193 of Applied Mathematical Sciences. Springer, New York (2015). [Google Scholar]
  13. L. Adam and J. Outrata, On optimal control of a sweeping process coupled with an ordinary differential equation. Discrete Contin. Dyn. Syst. Ser. B 19 (2014) 2709–2738. [Google Scholar]
  14. A.H. Siddiqi, P. Manchanda and M. Brokate, On some recent developments concerning Moreau's sweeping process, in Trends in Industrial and Applied Mathematics: Proceedings of the 1st International Conference on Industrial and Applied Mathematics of the Indian Subcontinent, Edited by A. H. Siddiqi and M. Kocvara. Springer, Boston, MA (2002) 339–354. [Google Scholar]
  15. M. Brokate and P. Krejčí, Weak differentiability of scalar hysteresis operators. Discrete Contin. Dyn. Syst. 35 (2015) 2405–2421. [Google Scholar]
  16. M. Brokate, Newton and Bouligand derivatives of the scalar play and stop operator. Math. Model. Nat. Phenom. 15 (2020) Art. 51. [Google Scholar]
  17. M. Brokate and P. Krejčí, A variational inequality for the derivative of the scalar play operator. J. Appl. Numer. Optim. 3 (2021) 263–283. [Google Scholar]
  18. L. Betz, Strong stationarity for optimal control of a nonsmooth coupled system: application to a viscous evolutionary variational inequality coupled with an elliptic PDE. SIAM J. Optim. 29 (2019) 3069–3099. [Google Scholar]
  19. J. Jarušek, M. Krbec, M. Rao and J. Sokołowski, Conical differentiability for evolution variational inequalities. J. Diff. Equ. 193 (2003) 131–146. [Google Scholar]
  20. A. Haraux, How to differentiate the projection on a convex set in Hilbert space. Some applications to variational inequalities. J. Math. Soc. Japan 29 (1977) 615–631. [Google Scholar]
  21. F. Mignot, Contrôle dans les inéquations variationelles elliptiques. J. Funct. Anal. 22 (1976) 130–185. [Google Scholar]
  22. C. Christof, Sensitivity analysis and optimal control of obstacle-type evolution variational inequalities. SIAM J. Control Optim. 57 (2019) 192–218. [Google Scholar]
  23. E.H. Zarantonello, Projections on convex sets in Hilbert space and spectral theory I and II. Contrib. Nonlinear Funct. Anal. (1971) 237–424. [Google Scholar]
  24. S. Adly and L. Bourdin, Sensitivity analysis of variational inequalities via twice epi-differentiability and proto-differentiability of the proximity operator. SIAM J. Optim. 28 (2018) 1699–1725. [Google Scholar]
  25. J.F. Bonnans, R. Cominetti and A. Shapiro, Sensitivity analysis of optimization problems under second order regular constraints. Math. Oper. Res. 23 (1998) 806–831. [Google Scholar]
  26. S. Fitzpatrick and R.R. Phelps, Differentiability of the metric projection in Hilbert space. Trans. Am. Math. Soc. 270 (1982) 483–501. [Google Scholar]
  27. D. Noll, Directional differentiability of the metric projection in Hilbert space. Pacific J. Math. 170 (1995) 567–592. [Google Scholar]
  28. A. Shapiro, Existence and differentiability of metric projections in Hilbert spaces. SIAM J. Optim. 4 (1994) 130–141. [Google Scholar]
  29. C.N. Do, Generalized second-order derivatives of convex functions in reflexive Banach spaces. Trans. Am. Math. Soc. 334 (1992) 281–301. [Google Scholar]
  30. C. Christof, Sensitivity Analysis of Elliptic Variational Inequalities of the First and the Second Kind. PhD thesis, Technische Universitat Dortmund (2018). [Google Scholar]
  31. C. Christof and G. Wachsmuth, Differential sensitivity analysis of variational inequalities with locally Lipschitz continuous solution operators. Appl. Math. Optim. 81 (2020) 23–62. [Google Scholar]
  32. T.H. Cao, N.T. Khalil, B.S. Mordukhovich, D. Nguyen, T. Nguyen and F.L. Pereira, Optimization of controlled free-time sweeping processes with applications to marine surface vehicle modeling. IEEE Control Syst. Lett. 6 (2022) 782–787. [Google Scholar]
  33. T.H. Cao and B.S. Mordukhovich, Optimal control of a perturbed sweeping process via discrete approximations. Discrete Contin. Dyn. Syst. Ser. B 21 (2016) 3331–3358. [Google Scholar]
  34. T.H. Cao and B.S. Mordukhovich, Optimal control of a nonconvex perturbed sweeping process. J. Diff. Equ. 266 (2019) 1003–1050. [Google Scholar]
  35. G. Colombo, R. Henrion, D.H. Nguyen and B.S. Mordukhovich, Optimal control of the sweeping process over polyhedral controlled sets. J. Diff. Equ. 260 (2016) 3397–3447. [Google Scholar]
  36. G. Colombo, B.S. Mordukhovich and D. Nguyen, Optimization of a perturbed sweeping process by constrained discontinuous controls. SIAM J. Control Optim. 58 (2020) 2678–2709. [Google Scholar]
  37. R. Henrion, A. Jourani and B.S. Mordukhovich, Controlled polyhedral sweeping processes: Existence, stability, and optimality conditions. J. Diff. Equ. 366 (2023) 408–443. [Google Scholar]
  38. C.E. Arroud and G. Colombo, A maximum principle for the controlled sweeping process. Set-Valued Var. Anal. 26 (2018) 607–629. [Google Scholar]
  39. M. Brokate and P. Krejčí, Optimal control of ODE systems involving a rate independent variational inequality. Discrete Contin. Dyn. Syst. Ser. B 18 (2013) 331–348. [Google Scholar]
  40. M.d.R. de Pinho, M.M.A. Ferreira and G.V. Smirnov, Optimal control involving sweeping processes. Set-Valued Var. Anal. 27 (2019) 523–548. [Google Scholar]
  41. R. Herzog, D. Knees, C. Meyer, M. Sievers, A. Stötzner and S. Thomas. Rate-independent systems and their viscous regularizations: analysis, simulation, and optimal control, in Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, edited by M. Hintermuöller, R. Herzog, C. Kanzow, M. Ulbrichand S. Ulbrich. Springer, Cham (2022) 121–144. [Google Scholar]
  42. C. Nour and V. Zeidan, Optimal control of nonconvex sweeping processes with separable endpoints: nonsmooth maximum principle for local minimizers. J. Diff. Equ. 318 (2022) 113–168. [Google Scholar]
  43. U. Stefanelli, D. Wachsmuth and G. Wachsmuth, Optimal control of a rate-independent evolution equation via viscous regularization. Discrete Contin. Dyn. Syst. Ser. S 10 (2017) 1467–1485. [Google Scholar]
  44. C. Christof, C. Meyer, B. Schweizer and S. Turek, Strong stationarity for optimal control of variational inequalities of the second kind, in Non-Smooth and Complementarity-Based Distributed Parameter Systems: Simulation and Hierarchical Optimization, edited by M. Hintermuöller, R. Herzog, C. Kanzow, M. Ulbrich and S. Ulbrich. Springer, Cham (2022) 307–327. [Google Scholar]
  45. F. Harder and G. Wachsmuth, Comparison of optimality systems for the optimal control of the obstacle problem. GAMM-Mitt. 40 (2018) 312–338. [Google Scholar]
  46. M. Hintermuöller and I. Kopacka, Mathematical programs with complementarity constraints in function space: C- and strong stationarity and a path-following algorithm. SIAM J. Optim. 20 (2008) 868–902. [Google Scholar]
  47. F. Mignot and J.P. Puel, Optimal control in some variational inequalities. SIAM J. Control Optim. 22 (1984) 466–476. [Google Scholar]
  48. M. Brokate and C. Christof, Strong stationarity conditions for optimal control problems governed by a rate-independent evolution variational inequality. SIAM J. Control Optim. 61 (2023) 2222–2250. [Google Scholar]
  49. P. Krejčí and V. Recupero, Comparing BV solutions of rate independent processes. J. Convex Anal. 21 (2014) 121–146. [Google Scholar]
  50. H. Attouch, G. Buttazzo and G. Michaille, Variational Analysis in Sobolev and BV Spaces. SIAM, Philadelphia (2006). [Google Scholar]
  51. C. Christof and G. Wachsmuth, Lipschitz stability and Hadamard directional differentiability for elliptic and parabolic obstacle-type quasi-variational inequalities. SIAM J. Control Optim. 60 (2022) 3430–3456. [Google Scholar]
  52. G.A. Monteiro, A. Slavík and M. Tvrdý, Kurzweil-Stieltjes Integral: Theory and Applications, vol. 15 of Series in Real Analysis. World Scientific, Singapore (2019). [Google Scholar]
  53. W. Bruns and J. Gubeladze, Polytopes, Rings, and K-Theory. Springer Monographs in Mathematics. Springer, New York (2009). [Google Scholar]
  54. M. Berger, M. Cole and S. Levy, Geometry II. Universitext. Springer, Berlin, Heidelberg (2009). [Google Scholar]
  55. U. Faigle, W. Kern and G. Still, Algorithmic Principles of Mathematical Programming. Texts in the Mathematical Sciences. Springer (2002). [Google Scholar]
  56. O.L. Mangasarian, Nonlinear Programming, vol. 10 of SIAM's Classics in Applied Mathematics, 2nd edn. SIAM (1994). [Google Scholar]
  57. L.C. Evans, Partial Differential Equations, 2nd edn. AMS, Providence, RI (2010). [Google Scholar]
  58. C. Christof and G. Wachsmuth, No-gap second-order conditions via a directional curvature functional. SIAM J. Optim. 28 (2018) 2097–2130. [CrossRef] [MathSciNet] [Google Scholar]
  59. G. Wachsmuth, A guided tour of polyhedric sets: basic properties, new results on intersections and applications. J. Convex Anal. 26 (2019) 153–188. [Google Scholar]
  60. G. Wachsmuth, Pointwise constraints in vector-valued Sobolev spaces: with applications in optimal control. Appl. Math. Optim. 77 (2018) 463–497. [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.