Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 73, 2024 - Issue 7
165
Views
0
CrossRef citations to date
0
Altmetric
Research Article

On the sum rules and maximality of generalized subdifferentials

&
Pages 2139-2158 | Received 16 Jul 2022, Accepted 28 Feb 2023, Published online: 17 Apr 2023

References

  • Borwein JM. Fifty years of maximal monotonicity. Optim Lett. 2010;4(4):473–490.
  • Alizadeh MH, Hadjisavvas N, Roohi M. Local boundedness properties for generalized monotone operators. J Convex Anal. 2012;19:49–61.
  • Iusem AN. An existence result for equilibrium problems with some surjectivity consequences. J Convex Anal. 2009;16:807–826.
  • Alizadeh MH. Fitzpatrick function for generalized monotone operators. J Nonlinear Convex Anal (to appear).
  • Alizadeh MH, Roohi M. Some results on pre-monotone operators. Bull Iranian Math Soc. 2017;43:2085–2097.
  • Iusem AN, Sosa W. On diametrically maximal sets, maximal premonotone operators and bifunctions. J Nonlinear Var Anal. 2020;4:253–271.
  • Jofré A. ϵ-subdifferential and ϵ-monotonicity. Nonlinear Anal. 1998;33(1):71–90.
  • Luc DT, Ngai HV, Théra M. Approximate convex functions. J Nonlinear Convex Anal. 2000;1(2):155–176.
  • Luc DT, Ngai HV, Théra M. On ϵ-monotonicity and ϵ-convexity. In: Ioffe A, et al., editors, Calculus of variations and differential equations (Haifa, 1998), Res. Notes Math. Ser. Vol. 410, Boca Raton: Chapman & Hall; 1999. p. 82–100.
  • Jourani A. Subdifferentiability and subdifferential monotonicity of γ-paraconvex functions. Control Cyber. 1996;25:721–737.
  • Alizadeh MH. On generalized convex functions and generalized subdifferential II. Optim Lett. 2021;15(6):2225–2240.
  • Alizadeh MH. On generalized convex functions and generalized subdifferential. Optim Lett. 2020;14(1):157–169.
  • Huang H, Sun C. Sigma-subdifferential and its application to minimization problem. Positivity. 2020;24(3):539–551.
  • Zălinescu C. Convex analysis in general vector spaces. World Scientific; 2002.
  • Alizadeh MH. On e-convex functions and e-subdifferentials in locally convex spaces, Optimization, (first online), https://doi.org/10.1080/02331934.2021.2015769
  • Morduklhovich BS, Nam NM. An easy path to convex analysis and applications. St Rafael: Morgan & Claypool Publishers; 2014.
  • Clarke FH. Optimization and nonsmooth analysis. New York: Wiley; 1983.
  • Phelps RR. Lectures on maximal monotone operators. Extracta Math. 1997;12:193–230.
  • Ivanov M, Zlateva N. Abstract subdifferential calculus and semi-convex functions. Serdica Math J. 1997;23(1):35–58.
  • Phelps R. Convex functions, monotone operators and differentiability. 2nd ed. Berlin: Springer; 1993.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.