Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 100, 2021 - Issue 3
Submit an article Journal homepage
102
Views
0
CrossRef citations to date
0
Altmetric
Articles

Disconnectedness and unboundedness of the solution sets of monotone vector variational inequalities

Vu Trung HieuDivision of Mathematics, Phuong Dong University, Hanoi, VietnamCorrespondence[email protected]
ORCID Iconhttps://orcid.org/0000-0001-5775-9788View further author information
ORCID Icon
Pages 482-492 | Received 12 Jul 2018, Accepted 09 Apr 2019, Published online: 01 May 2019

References

  • Giannessi F. Theorems of alternative, quadratic programs and complementarity problems. In: Cottle RW, Giannessi F, Lions J-L, editors. Variational inequality and complementarity problems. New York (NY): Wiley; 1980. p. 151–186.
  • Hieu VT. Numbers of the connected components of the solution sets of monotone affine vector variational inequalities. J Glob Optim. 2019;73:223–237. doi: 10.1007/s10898-018-0678-2
  • Lee GM, Kim DS, Lee BS, et al. Vector variational inequalities as a tool for studying vector optimization problems. Nonlinear Anal. 1998;34:745–765. doi: 10.1016/S0362-546X(97)00578-6
  • Yen ND, Lee GM. On monotone and strongly monotone vector variational inequalities. In: Giannessi F, editor. Vector variational inequalities and vector equilibria. nonconvex optimization and its applications, Vol 38. Boston (MA): Springer; 2000. p. 467–478.
  • Yen ND, Phuong TD. Connectedness and stability of the solution sets in linear fractional vector optimization problems. In: Giannessi F, editor. Vector variational inequalities and vector equilibria. nonconvex optimization and its applications, Vol 38. Boston (MA): Springer; 2000. p. 479–489.
  • Yen ND, Yao J-C. Monotone affine vector variational inequalities. Optimization. 2011;60:53–68. doi: 10.1080/02331934.2010.505650
  • Robinson SM. Generalised equations and their solutions, part I: Basic theory. Math Program Study. 1979;10:128–141. doi: 10.1007/BFb0120850
  • Facchinei F, Pang J-S. Finite-dimensional variational inequalities and complementarity problems. New York (NY): Springer-Verlag; 2003.
  • Chen GY, Yang XQ. The vector complementarity problems and their equivalence with the weak minimal element in ordered spaces. J Math Anal Appl. 1990;153:136–158. doi: 10.1016/0022-247X(90)90223-3
  • Lee GM, Yen ND. A result on vector variational inequalities with polyhedral constraint sets. J Optim Theory Appl. 2001;109:193–197. doi: 10.1023/A:1017522107088
  • Huong NTT, Yao J-C, Yen ND. Polynomial vector variational inequalities under polynomial constraints and applications. SIAM J Optim. 2016;26:1060–1071. doi: 10.1137/15M1041134

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:

Order Reprints Request Corporate Permissions

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:

Request Academic Permissions

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.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.