Publication Cover
Optimization
A Journal of Mathematical Programming and Operations Research
Volume 73, 2024 - Issue 6
406
Views
4
CrossRef citations to date
0
Altmetric
Research Article

A dynamical system for solving inverse quasi-variational inequalities

ORCID Icon & ORCID Icon
Pages 1681-1701 | Received 11 Apr 2022, Accepted 19 Jan 2023, Published online: 02 Feb 2023

References

  • He B, He X, Liu HX. Solving a class of constrained ‘black-box’ inverse variational inequalities. Eur J Oper Res. 2010;204(3):391–401.
  • Aussel D, Gupta R, Mehra A. Gap functions and error bounds for inverse quasi-variational inequality problem. J Math Anal Appl. 2013;407:270–280.
  • Han Y, Huang N, Lu J, et al. Existence and stability of solutions to inverse variational inequality problems. Appl Math Mech. 2017;38(5):749–764.
  • He X, Liu HX. Inverse variational inequalities with projection-based solution methods. Eur J Oper Res. 2011;208:12–18.
  • Kinderlehrer D, Stampacchia G. An introduction to variational inequalities and their applications. New York: SIAM Academic Press; 1980.
  • Stampacchia G. Formes bilineaires coercitives sur les ensembles convexes. C R Acad Sci Paris. 1964;258:4413–4416.
  • Censor Y, Gibali A, Reich S. Algorithms for the split variational inequality problem. Numer Algorithms. 2012;59:301–323.
  • Dong QL, Lu YY, Yang J, et al. Approximately solving multi-valued variational inequalities by using a projection and contraction algorithm. Numer Algorithms. 2017;76(3):799–812.
  • Facchinei F, Pang JS. Finite-dimensional variational inequalities and complementarity problems. Vol. I, New York: Springer; 2003.
  • Noor MD. Well-posed variational inequalities. J Appl Math Comput. 2003;11(1–2):165–172.
  • Yamada H. The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings. Inher Paral Algorithms Feasib Optim Their Appl. 2001;8(1):473–504.
  • Censor Y, Gibali A, Reich S. Strong convergence of subgradient extragradient methods for the variational inequality problem in Hilbert space. Optim Methods Softw. 2011;26:827–845.
  • Censor Y, Gibali A, Reich S. The subgradient extragradient method for solving variational inequalities in Hilbert space. J Optim Theory Appl. 2011;148:318–335.
  • He BS. A class of projection and contraction methods for monotone variational inequalities. Appl Math Optim. 1997;35:69–76.
  • Dong QL, Yang JF, Yuan HB. The projection and contraction algorithm for solving variational inequality problems in Hilbert space. J Nonlinear Convex Anal. 2019;20(1):111–122.
  • Dey S, Vetrivel V, Xu HK. A neural network method for monotone variational inclusions. J Nonlinear Convex Anal. 2019;20(11):2387–2395.
  • Mijajlovi N, Jacimovi M, Noor MA. Gradient-type projection methods for quasi-variational inequalities. Optm Lett. 2019;13:1885–1896.
  • Nesterov Y, Scrimali L. Solving strongly monotone variational and quasi-variational inequalities. Discrete Contin Dyn Syst. 2011;31(4):1383–1396.
  • Zou X, Gong D, Wang L, et al. A novel method to solve inverse variational inequality problems based on neural networks. Neurocomputing. 2016;173:1163–1168.
  • Hu X, Wang J. Solving the assignment problem using continuous-time and discrete-time improved dual network. IEEE Trans Neural Netw Learn Syst. 2012;23:821–827.
  • Hu R, Fang Y-P. Levitin–Polyak well-posedness by perturbations for the split inverse variational inequality problem. J Fixed Point Theory Appl. 2016;18(4):785–800.
  • Noor MA. Quasi variational inequalities. Appl Math Lett. 1988;1(4):367–370.
  • Dey S, Vetrivel V. On approximate solution to the inverse quasi-variational inequality problem. Sci Math Jpn. 2018;81(3):301–306.
  • Chang SS, Wang XR, Tang JF. Error bounds for generalized vector inverse quasi-variational inequality problems with point to set mappings. AIMS Math. 2021;6(2):1800–1815.
  • Wang ZB, Chen ZY, Chen Z. Gap functions and error bounds for vector inverse mixed quasi-variational inequality problems. Fixed Point Theory Appl. 2019;14:14.
  • Gao XB, Liao LZ, Qi L. A novel neural network for variational inequalities with linear and nonlinear constraints. IEEE Trans Neural Netw. 2005;16(6):1305–1317.
  • Nguyen LV, Qin X. Some results on strongly pseudomonotone quasi-variational inequalities. Set-Valued Var Anal. 2020;28:239–257.
  • Xu HK, Dey S, Vetrivel V. Notes on a neural network approach to inverse variational inequalities. Optimization. 2021;70(5–6):901–910.
  • Bauschke HH, Combettes PL. Convex analysis and monotone operator theory in Hilbert spaces. New York: Springer; 2011.
  • Beesack P. Gronwall inequalities. Ottawa: Carleton University; 1975. (Carleton mathematical lecture notes no. 11).
  • Noor MA. An iterative scheme for a class of quasi-variational inequalities. J Math Anal Appl. 1985;110:463–468.
  • Hartman P. Ordinary differential equations, classics in applied mathematics. Vol. 18, Philadelphia: SIAM; 2002.

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.