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All issues Volume 30 (2024) ESAIM: COCV, 30 (2024) 83 References
Open Access
Issue
ESAIM: COCV
Volume 30, 2024
Article Number 83
Number of page(s) 25
DOI https://doi.org/10.1051/cocv/2024070
Published online 25 October 2024
  1. J.-P. Aubin and H. Frankowska, Set-valued Analysis. Birkhaüser, Boston (1991). [Google Scholar]
  2. M. Benko, H. Gfrerer and J.V. Outrata, Calculus for directional limiting normal cones and subdifferentials. Set-Valued Variat. Anal. 27 (2019) 713–745. [CrossRef] [Google Scholar]
  3. J.F. Bonnans and A. Shapiro, Perturbation Analysis of Optimization Problems, 1st edn. Springer-Verlag, New York (2000). [Google Scholar]
  4. T.D. Chuong and D.S. Kim, Holder-like property and metric regularity of a positive-order for implicit multifunctions. Math. Oper. Res. 41 (2016) 596–611. [CrossRef] [MathSciNet] [Google Scholar]
  5. A.L. Dontchev and R.T. Rockafellar, Implicit Functions and Solution Mappings, A View from Variational Analysis, 2nd edn. Springer, New York (2014). [CrossRef] [Google Scholar]
  6. 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]
  7. H. Gfrerer and J.V. Outrata, On Lipschitzian properties of implicit multifunctions. SIAM J. Optim. 26 (2016) 2160–2189. [CrossRef] [MathSciNet] [Google Scholar]
  8. A.D. Ioffe, On regularity concepts in variational analysis. J. Fixed Point Theory Appl. 8 (2010) 339–363. [CrossRef] [MathSciNet] [Google Scholar]
  9. B.S. Mordukhovich, Complete characterization of openness, metric regularity, and Lipschitzian properties of multifunctions. Trans. Amer. Math. Soc. 340 (1993) 1–35. [CrossRef] [MathSciNet] [Google Scholar]
  10. B.S. Mordukhovich, Variational Analysis and Generalized Differentiation. I. Basic Theory. Springer-Verlag, Berlin (2006). [Google Scholar]
  11. R.A. Poliquin and R.T. Rockafellar, Tilt stability of a local minimum. SIAM J. Optim. 8 (1998) 287–299. [CrossRef] [MathSciNet] [Google Scholar]
  12. R.T. Rockafellar, Convex Analysis. Princeton University Press, Princeton (1996). [Google Scholar]
  13. N.D. Yen, Lipschitz continuity of solutions of variational inequalities with a parametric polyhedral constraint. Math. Oper. Res. 20 (1995) 695–708. [CrossRef] [MathSciNet] [Google Scholar]
  14. H.V. Ngai, N.H. Tron and M. Théra, Metric regularity relative to a cone. Vietnam J. Math. 47 (2019) 733–756. [CrossRef] [MathSciNet] [Google Scholar]
  15. A.V. Arutyunov and A.F. Izmailov, Directional stability theorem and directional metric regularity. Math. Oper. Res. 31 (2006) 526–543. [CrossRef] [MathSciNet] [Google Scholar]
  16. M. Durea, M. Pantiruc and R. Stugariu, A new type of directional regularity for mappings and applications to optimization. SIAM J. Optim. 27 (2017) 12004–1229. [Google Scholar]
  17. H.V. Ngai and M. Théra, Directional metric regularity of multifunctions. Math. Oper. Res. 40 (2015) 797–1088. [CrossRef] [MathSciNet] [Google Scholar]
  18. K.W. Meng, M.H. Li, W.F. Yao and X.Q. Yang, Lipschitz-like property relative to a set and the generalized Mordukhovich criterion. Math. Program. 189 (2021) 45–489. [Google Scholar]
  19. X. Qin, V.D. Thinh and J.-C. Yao, On new generalized differentials relative to a set and their applications. Set-Valued Variat. Anal. 32 (2024) 27. [CrossRef] [Google Scholar]
  20. R.T. Rockafellar and R.-B. Wet, Variational Analysis. Springer, Berlin (1998). [CrossRef] [Google Scholar]
  21. W. Yao and X. Yang, Relative Lipschitz-like property of parametric systems via projectional coderivative. SIAM J. Optim. 3 (2023) 2021–2040. [CrossRef] [MathSciNet] [Google Scholar]
  22. B.S. Mordukhovich, P. Wu and X. Yang, Relative well-posedness of constrained systems with applications to variational inequalities (2024), https://arxiv.org/abs/2212.02727 [Google Scholar]
  23. V.D. Thinh, X. Qin and J.-C. Yao, Formulas for calculating of generalized differentials relative to a set and their applications (2023), https://arxiv.org/pdf/2311.08741.pdf [Google Scholar]
  24. V.D. Thinh, X. Qin and J.-C. Yao, Coderivatives relative to a set of the normal cone mappings and their applications (2023), http://arxiv.org/abs/2312.15834 [Google Scholar]
  25. E.H. Clarke, Y.S. Ledyaev, R.J. Stem and R.R. Wolenski, Nonsmooth Analysis and Control Theory. Springer-Verlag, New York (1998). [Google Scholar]
  26. W. Yao, K. Meng, M. Li and X. Yang, Projectional coderivatives and calculus rules. Set-Valued Variat. Anal. 31 (2023) 36. [CrossRef] [Google Scholar]

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