EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 42 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 42
Number of page(s) 35
DOI https://doi.org/10.1051/cocv/2022024
Published online 29 June 2022
  1. R. Andreani, N.S. Fazzio, M.L. Schuverdt and L.D. Secchin, A sequential optimality condition related to the quasi-normality constraint qualification and its algorithmic consequences. SIAM J. Optim. 29 (2019) 743–766. [CrossRef] [MathSciNet] [Google Scholar]
  2. R. Andreani, G. Haeser and J.M. Martinez, On sequential optimality conditions for smooth constrained optimization. Optimization 60 (2011) 627–641. [CrossRef] [MathSciNet] [Google Scholar]
  3. R. Andreani, G. Haeser, L.D. Secchin and P.J.S. Silva, New sequential optimality conditions for mathematical programs with complementarity constraints and algorithmic consequences. SIAM J. Optim. 29 (2019) 3201–3230. [CrossRef] [MathSciNet] [Google Scholar]
  4. R. Andreani, G. Haeser and D.S. Viana, Optimality conditions and global convergence for nonlinear semidefinite programming. Math. Program. 180 (2020) 203–235. [CrossRef] [MathSciNet] [Google Scholar]
  5. R. Andreani, J.M. Martinez, A. Ramos and P.J.S. Silva, A cone-continuity constraint qualification and algorithmic consequences. SIAM J. Optim. 26 (2016) 96–110. [CrossRef] [MathSciNet] [Google Scholar]
  6. R. Andreani, J.M. Martinez and B.F. Svaiter, A new sequential optimality condition for constrained optimization and algorithmic consequences. SIAM J. Optim. 20 (2010) 3533–3554. [CrossRef] [MathSciNet] [Google Scholar]
  7. J.-P. Aubin and H. Frankowska, Set-Valued Analysis. Birkhauser, Boston (2009). [Google Scholar]
  8. K. Bai, J.J. Ye and J. Zhang, Directional quasi-/pseudo-normality as sufficient conditions for metric subregularity. SIAM J. Optim. 29 (2019) 2625–2649. [CrossRef] [MathSciNet] [Google Scholar]
  9. E.G. Birgin and J.M. Martinez, Practical Augmented Lagrangian Methods for Constrained Optimization. SIAM, Philadelphia (2014). [Google Scholar]
  10. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems. Springer, New York (2000). [Google Scholar]
  11. E. Borgens, C. Kanzow, P. Mehlitz and G. Wachsmuth, New constraint qualifications for optimization problems in Banach spaces based on asymptotic KKT conditions. SIAM J. Optim. 30 (2020) 2956–2982. [CrossRef] [MathSciNet] [Google Scholar]
  12. E. Borgens, C. Kanzow and D. Steck, Local and global analysis of multiplier methods for constrained optimization in Banach spaces. SIAM J. Control Optim. 57 (2019) 3694–3722. [CrossRef] [MathSciNet] [Google Scholar]
  13. J.M. Borwein and Q.J. Zhu, Techniques of Variational Analysis. Springer, New York (2005). [Google Scholar]
  14. K. Bredies and D. Lorenz, Mathematical Image Processing. Birkhauser, Cham (2018). [Google Scholar]
  15. X. Chen, L. Guo, Z. Lu and J.J. Ye, An augmented Lagrangian method for non-Lipschitz nonconvex programming. SIAM J. Numer. Anal. 55 (2017) 168–193. [CrossRef] [MathSciNet] [Google Scholar]
  16. C. Christof, C. Meyer, S. Walther and C. Clason, Optimal control of a non-smooth semilinear elliptic equation. Math. Control Related Fields 8 (2018) 247–276. [CrossRef] [MathSciNet] [Google Scholar]
  17. 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. [CrossRef] [MathSciNet] [Google Scholar]
  18. C. Clason, A. Rund and K. Kunisch, Nonconvex penalization of switching control of partial differential equations. Syst. Control Lett. 106 (2017) 1–8. [CrossRef] [Google Scholar]
  19. Y. Deng, P. Mehlitz and U. Pruüfert, Coupled versus decoupled penalization of control complementarity constraints. ESAIM: COCV 27 (2021) 1–31. [CrossRef] [EDP Sciences] [Google Scholar]
  20. A.L. Dontchev, H. Gfrerer, A.Y. Kruger and J.V. Outrata, The radius of metric subregularity. Set-Valued Variat. Anal. 28 (2020) 451–472. [CrossRef] [Google Scholar]
  21. A.L. Dontchev and R.T. Rockafellar, Implicit Functions and Solution Mappings, Springer, New York (2014). [Google Scholar]
  22. I. Ekeland, On the variational principle. J. Math. Anal. Appl. 47 (1974) 324–353. [CrossRef] [MathSciNet] [Google Scholar]
  23. M.J. Fabian, Subdifferentiability and trustworthiness in the light of a new variational principle of Borwein and Preiss. Acta Univer. Carol. 30 (1989) 51–56. [Google Scholar]
  24. M.J. Fabian, R. Henrion, A.Y. Kruger and J.V. Outrata, Error bounds: necessary and sufficient conditions. Set-Valued Variat. Anal. 18 (2010) 121–149. [CrossRef] [Google Scholar]
  25. M.L. Flegel, C. Kanzow and J.V. Outrata, Optimality conditions for disjunctive programs with application to mathematical programs with equilibrium constraints. Set-Valued Anal. 15 (2007) 139–162. [CrossRef] [MathSciNet] [Google Scholar]
  26. H. Gfrerer, On directional metric regularity, subregularity and optimality conditions for nonsmooth mathematical programs. Set-Valued Variat. Anal. 21 (2013) 151–176. [CrossRef] [Google Scholar]
  27. L. Guo, G.-H. Lin and J.J. Ye, Solving mathematical programs with equilibrium constraints. J. Optim. Theory Appl. 166 (2015) 234–256. [CrossRef] [MathSciNet] [Google Scholar]
  28. L. Guo and J.J. Ye, Necessary optimality conditions and exact penalization for non-Lipschitz nonlinear programs. Math. Program. 168 (2018) 571–598. [CrossRef] [MathSciNet] [Google Scholar]
  29. F. Harder, P. Mehlitz and G. Wachsmuth, Reformulation of the M-stationarity conditions as a system of discontinuous equations and its solution by a semismooth Newton method. SIAM J. Optim. 31 (2021) 1459–1488. [CrossRef] [MathSciNet] [Google Scholar]
  30. F. Harder and G. Wachsmuth, Comparison of optimality systems for the optimal control of the obstacle problem. GAMMMitteilungen 40 (2018) 312–338. [Google Scholar]
  31. E.S. Helou, S.A. Santos and L.E.A. Simoes, A new sequential optimality condition for constrained nonsmooth optimization. SIAM J. Optim. 30 (2020) 1610–1637. [CrossRef] [MathSciNet] [Google Scholar]
  32. M. Hintermuüller, 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. [CrossRef] [MathSciNet] [Google Scholar]
  33. A.D. Ioffe, Variational Analysis of Regular Mappings. Theory and Applications. Springer, Cham (2017). [Google Scholar]
  34. K. Ito and K. Kunisch, Optimal control with Lp(Q), p € [0,1), control cost. SIAM J. Control Optim. 52 (2014) 1251–1275. [CrossRef] [MathSciNet] [Google Scholar]
  35. X. Jia, C. Kanzow, P. Mehlitz and G. Wachsmuth, An augmented Lagrangian method for optimization problems with structured geometric constraints. Tech. rep., preprint arXiv (2021) https://arxiv.org/abs/2105.08317. [Google Scholar]
  36. C. Kanzow, A.B. Raharja and A. Schwartz, Sequential optimality conditions for cardinality-constrained optimization problems with applications. Comput. Optim. Appl. 80 (2021) 185–211. [CrossRef] [MathSciNet] [Google Scholar]
  37. C. Kanzow and D. Steck, An example comparing the standard and safeguarded augmented Lagrangian methods. Oper. Res. Lett. 45 (2017) 598–603. [CrossRef] [MathSciNet] [Google Scholar]
  38. C. Kanzow, D. Steck and D. Wachsmuth, An augmented Lagrangian method for optimization problems in Banach spaces. SIAM J. Optim. 56 (2018) 272–291. [CrossRef] [MathSciNet] [Google Scholar]
  39. D. Klatte and B. Kummer, Nonsmooth Equations in Optimization. Regularity, Calculus, Methods and Applications, Kluwer Academic, Dordrecht (2002). [Google Scholar]
  40. A.Y. Kruger, Generalized differentials of nonsmooth functions and necessary conditions for an extremum. Sibirian Math. J. 26 (1985) 370–379. [Google Scholar]
  41. A.Y. Kruger, On Fréchet subdifferentials. J. Math. Sci. (New York) 116 (2003) 3325–3358. [CrossRef] [MathSciNet] [Google Scholar]
  42. A.Y. Kruger, About stationarity and regularity in variational analysis. Taiwan. J. Math. 13 (2009) 1737–1785. [Google Scholar]
  43. A.Y. Kruger, Error bounds and metric subregularity. Optimization 64 (2015) 49–79. [CrossRef] [MathSciNet] [Google Scholar]
  44. A.Y. Kruger and B.S. Mordukhovich, Extremal points and the Euler equation in nonsmooth optimization problems. Doklady Akademii Nauk BSSR 24 (1980) 684–687. [MathSciNet] [Google Scholar]
  45. M. Maréchal, Metric subregularity in generalized equations. J. Optim. Theory Appl. 176 (2018) 541–558. [CrossRef] [MathSciNet] [Google Scholar]
  46. P. Mehlitz, On the sequential normal compactness condition and its restrictiveness in selected function spaces. Set-Valued Variat. Anal. 27 (2019) 763–782. [CrossRef] [Google Scholar]
  47. P. Mehlitz, Asymptotic stationarity and regularity for nonsmooth optimization problems. J. Nonsmooth Anal. Optim. 1 (2020) 6575. [Google Scholar]
  48. P. Mehlitz, Asymptotic regularity for Lipschitzian nonlinear optimization problems with applications to complementarity- constrained and bilevel programming. Optimization (2022) 1–44. [Google Scholar]
  49. P. Mehlitz and G. Wachsmuth, The limiting normal cone to pointwise defined sets in Lebesgue spaces. Set-Valued Variat. Anal. 26 (2018) 449–467. [CrossRef] [Google Scholar]
  50. P. Mehlitz and G. Wachsmuth, Subdifferentiation of nonconvex sparsity-promoting functionals on Lebesgue spaces. SIAM J. Control Optim. (2022) 1–22. [Google Scholar]
  51. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation, Part I: Basic Theory, Part II: Applications. Springer, Berlin (2006). [Google Scholar]
  52. C. Natemeyer and D. Wachsmuth, A proximal gradient method for control problems with nonsmooth and nonconvex control cost. Comput. Optim. Appl. 80 (2021) 639–677. [CrossRef] [MathSciNet] [Google Scholar]
  53. J.-P. Penot, Calculus Without Derivatives. Springer, New York (2013). [Google Scholar]
  54. R.R. Phelps, Convex Functions, Monotone Operators and Differentiability. Springer, Berlin (1993). [Google Scholar]
  55. A. Ramos, Mathematical programs with equilibrium constraints: a sequential optimality condition, new constraint qualifications and algorithmic consequences. Optim. Methods Softw. 36 (2021) 45–81. [CrossRef] [MathSciNet] [Google Scholar]
  56. A.-T. Rauls and G. Wachsmuth, Generalized derivatives for the solution operator of the obstacle problem. Set-Valued Variat. Anal. 28 (2020) 259–285. [CrossRef] [Google Scholar]
  57. R.T. Rockafellar and R.J.B. Wets, Variational Analysis. Springer, Berlin (1998). [Google Scholar]
  58. L. Thibault, Sequential convex subdifferential calculus and sequential Lagrange multipliers. SIAM J. Control Optim. 35 (1997) 1434–1444. [CrossRef] [MathSciNet] [Google Scholar]
  59. D. Wachsmuth, Iterative hard-thresholding applied to optimal control problems with L°(Q) control cost. SIAM J. Control Optim. 57 (2019) 854–879. [CrossRef] [MathSciNet] [Google Scholar]
  60. C. Zalinescu, Convex Analysis in General Vector Spaces. World Scientific, River Edge (2002). [Google Scholar]
  61. X.Y. Zheng and K.F. Ng, Metric subregularity and calmness for nonconvex generalized equations in Banach spaces. SIAM J. Optim. 20 (2010) 2119–2136. [CrossRef] [MathSciNet] [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.