We extend gap functions to quasi-equilibrium problems by using the duality results. In particular, we obtain new results for quasi-equilibrium problems known earlier for equilibrium problems and mixed quasi-variational inequalities.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
E. Blum and W. Oettli, “From optimization and variational inequalities to equilibrium problems,” Math Stud. 63, No. 1-4, 123-145 (1994).
D. Aussel and J. Cotrina, “An existence result for quasi-equilibrium problems,” J. Convex Anal. 24, No. 1, 55-66 (2017).
J. Cotrina and J. Zúñiga, “A note on quasi-equilibrium problems,” textitOper. Res. Lett. 46, No. 1, 138-140 (2018).
G. Bigi and M. Passacantando, “Gap functions for quasi-equilibria,” J. Glob. Optim. 66, No. 4, 791-810 (2016).
P. J. S. Santos, P. S. M. Santos, and S. Scheimberg, “A Newton-type method for quasiequilibrium problems and applications,” Optimization 71, No. 1, 7-32 (2022).
L. Altangerel, “Gap functions for quasi-variational inequalities via duality,” J. Inequal. Appl. Paper No. 13 (2018).
M. Fukushima, “A class of gap functions for quasi-variational inequality problems,” J. Ind. Manag. Optim. 3, No. 2, 165-171 (2007).
K. Taji, “On gap functions for quasi-variational inequalities,” Abstr. Appl. Anal. 2008, Article ID 631361 (2008).
R. I. Bot¸ and E. R. Csetnek, “Conjugate duality and the control of linear discrete systems,” J. Optim. Theory Appl. 159, No. 3, 576-589 (2013).
L. Altangerel, R. I. Bot¸, and G. Wanka, “On gap functions for equilibrium problems via Fenchel duality,” Pac. J. Optim. 2, No. 3, 667-678 (2006).
L. Altangerel, R. I. Bot¸, and G.Wanka, “On the construction of gap functions for variational inequalities via conjugate duality,” Asia-Pac. J. Oper. Res. 24, No. 3, 353-371 (2007).
L. F. Bueno, G. Haeser, F. Lara, and F. N. Rojas, “An augmented Lagrangian method for quasi-equilibrium problems,” Comput. Optim. Appl. 76, No. 3, 737-766 (2020).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Altangere, L. On Gap Functions for Quasi-Equilibrium Problems Via Duality. J Math Sci 279, 730–737 (2024). https://doi.org/10.1007/s10958-024-07055-7
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-024-07055-7