Open Access
Issue
ESAIM: COCV
Volume 32, 2026
Article Number 61
Number of page(s) 19
DOI https://doi.org/10.1051/cocv/2026043
Published online 14 July 2026
  1. A. Brøndsted and R.T. Rockafellar, On the subdifferentiability of convex functions. Proc. Am. Math. Soc. 16 (1965) 605–611. [Google Scholar]
  2. E. Bishop and R.R. Phelps, The support functionals of a convex set, in Proc. Sympos. Pure Math., Vol. VII. American Mathematical Society, Providence, RI (1963) 27–35. [Google Scholar]
  3. I. Ekeland, On the variational principle. J. Math. Anal. Appl. 47 (1974) 324–353. [Google Scholar]
  4. G. Carlier, Fenchel-Young inequality with a remainder and applications to convex duality and optimal transport. SIAM J. Optim. 33 (2023) 1463–1472. [Google Scholar]
  5. S. Armeniakos and A. Daniilidis, Characterizing maximal monotone operators with unique representation. arXiv:2510.09368 (2025). [Google Scholar]
  6. H.H. Bauschke, S. Singh and X. Wang, On Carlier's inequality. J. Convex Anal. 30 (2023) 499–514. [Google Scholar]
  7. R.S. Burachik and J.E. Martínez-Legaz, A note on carlier's inequality. Optimization (2025) 1–6. [Google Scholar]
  8. R.I. Boţ and E.R. Csetnek, A Brø ndsted–Rockafellar theorem for diagonal subdifferential operators, in Computational and analytical mathematics, vol. 50 of Springer Proc. Math. Stat.. Springer, New York (2013) 105–112. [Google Scholar]
  9. A.N. Iusem and B.F. Svaiter, On diagonal subdifferential operators in nonreflexive Banach spaces. Set-Valued Var. Anal. 20 (2012) 1–14. [Google Scholar]
  10. M. Marques Alves and B.F. Svaiter, Brøndsted–Rockafellar property and maximality of monotone operators representable by convex functions in non-reflexive Banach spaces. J. Convex Anal. 15 (2008) 693–706. [Google Scholar]
  11. S. Simons, From Hahn–Banach to monotonicity, vol. 1693 of Lecture Notes in Mathematics, 2nd edn. Springer, New York (2008). [Google Scholar]
  12. T. Amahroq and A. Oussarhan, An extension of Brøndsted–Rockafellar's theorem with applications. J. Math. Anal. Appl. 531 (2024) Paper No. 127810, 10. [Google Scholar]
  13. Z. Chbani and H. Riahi, Variational principles for monotone and maximal bifunctions. Serdica Math. J. 29 (2003) 159–166. [Google Scholar]
  14. R. Correa, A. Hantoute and P. Pérez-Aros, On Brøndsted–Rockafellar's Theorem for convex lower semicontinuous epi-pointed functions in locally convex spaces. Math. Program. 168 (2018) 631–643. [Google Scholar]
  15. J. Falcó and D. Isert, Group invariant variational principles. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. 118 (2024) Paper No. 91, 20. [Google Scholar]
  16. M. Lassonde, Brøndsted–Rockafellar property of subdifferentials of prox-bounded functions. J. Convex Anal. 22 (2015) 485–492. [Google Scholar]
  17. X.Y. Zheng, Corrigendum: convex optimization problems on differentiable sets. SIAM J. Optim. 33 (2023) 24842488. [Google Scholar]
  18. L. Ambrosio, N. Gigli and G. Savaré, Gradient Flows in Metric Spaces and in the Space of Probability Measures. Lectures in Mathematics ETH Zurich, 2nd edn. Birkhauser Verlag, Basel (2008). [Google Scholar]
  19. L. Ambrosio and G. Savaré, Gradient flows of probability measures, in Handbook of differential equations: evolutionary equations, vol. III of Handbook of Differential Equations. Elsevier/North-Holland, Amsterdam (2007) 1–136. [Google Scholar]
  20. A.Y. Kruger, Error bounds and metric subregularity. Optimization 64 (2015) 49–79. [Google Scholar]
  21. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions. Trans. Am. Math. Soc. 215 (1976) 241–251. [Google Scholar]
  22. R. Cibulka, A.L. Dontchev and A.Y. Kruger, Strong metric subregularity of mappings in variational analysis and optimization. J. Math. Anal. Appl. 457 (2018) 1247–1282. [Google Scholar]
  23. A.L. Dontchev, H. Gfrerer, A.Y. Kruger and J.V. Outrata, The radius of metric subregularity. Set-Valued Var. Anal. 28 (2020) 451–473. [Google Scholar]
  24. A.L. Dontchev and R.T. Rockafellar, Implicit functions and solution mappings. Springer Series in Operations Research and Financial Engineering, 2nd edn. Springer, New York (2014). A view from variational analysis. [Google Scholar]
  25. N.A. Jork, N.P. Osmolovskii and V.M. Veliov, Strong metric (sub)regularity in optimal control. J. Convex Anal. 32 (2025) 375–398. [Google Scholar]
  26. F.J. Aragón Artacho and M.H. Geoffroy, Characterization of metric regularity of subdifferentials. J. Convex Anal. 15 (2008) 365–380. [MathSciNet] [Google Scholar]
  27. D. Azé and J.-N. Corvellec, Nonlinear local error bounds via a change of metric. J. Fixed Point Theory Appl. 16 (2014) 351–372. [Google Scholar]
  28. D. Azé and J.-N. Corvellec, Nonlinear error bounds via a change of function. J. Optim. Theory Appl. 172 (2017) 9–32. [Google Scholar]
  29. D. Hauer and J.M. Mazón, Kurdyka–Łojasiewicz–Simon inequality for gradient flows in metric spaces. Trans. Am. Math. Soc. 372 (2019) 4917–4976. [Google Scholar]
  30. A. Blanchet and J. Bolte, A family of functional inequalities: Lojasiewicz inequalities and displacement convex functions. J. Funct. Anal. 275 (2018) 1650–1673. [Google Scholar]
  31. A. Figalli and F. Glaudo, An Invitation to Optimal Transport, Wasserstein Distances, and Gradient Flows. EMS Textbooks in Mathematics. EMS Press, Berlin (2021). [Google Scholar]
  32. G. Wachsmuth, A convex, finite and lower semicontinuous function with empty subdifferential. J. Convex Anal. 32 (2025) 877–882. [Google Scholar]
  33. H. Attouch, G. Buttazzo and G. Michaille, Variational analysis in Sobolev and BV spaces, volume 17 of MOS-SIAM Series on Optimization, 2nd edn. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA; Mathematical Optimization Society, Philadelphia, PA (2014). Applications to PDEs and optimization. [Google Scholar]
  34. R. Jordan, D. Kinderlehrer and F. Otto, The variational formulation of the Fokker–Planck equation. SIAM J. Math. Anal. 29 (1998) 1–17. [CrossRef] [MathSciNet] [Google Scholar]
  35. M. Bačák and U. Kohlenbach, On proximal mappings with Young functions in uniformly convex Banach spaces. J. Convex Anal. 25 (2018) 1291–1318. [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.