Skip to main content

Advertisement

SpringerLink
Log in

Qualitative properties of strongly pseudomonotone variational inequalities

  • Original Paper
  • Published:
Optimization Letters Aims and scope Submit manuscript

Abstract

Qualitative properties of strongly pseudomonotone variational inequalities such as solution existence, stability and global error bound are studied in this paper.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. El Farouq, N.: Pseudomonotone variational inequalities: convergence of proximal methods. J. Optim. Theory Appl. 109, 311–326 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  2. El Farouq, N.: Pseudomonotone variational inequalities: convergence of the auxiliary problem method. J. Optim. Theory Appl. 111, 305–326 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  3. El Farouq, N.: Convergent algorithm based on progressive regularization for solving pseudomonotone variational inequalities. J. Optim. Theory Appl. 120, 455–485 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  4. Facchinei, F., Pang, J.S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vol. I. II. Springer, New York (2003)

    MATH  Google Scholar 

  5. Huy, N.Q., Yen, N.D.: Minimax variational inequalities. Acta Math. Vietnam. 36, 265–281 (2011)

    MathSciNet  MATH  Google Scholar 

  6. Karamardian, S., Schaible, S.: Seven kinds of monotone maps. J. Optim. Theory Appl. 66, 37–46 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  7. Khanh, P.D., Vuong, P.T.: Modified projection method for strongly pseudomonotone variational inequalities. J. Global Optim. 58, 341–350 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kien, B.T., Lee, G.M.: An existence theorem for generalized variational inequalities with discontinuous and pseudomonotone operators. Nonlinear Anal. 74, 1495–1500 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  9. Kien, B.T., Yao, J.-C., Yen, N.D.: On the solution existence of pseudomonotone variational inequalities. J. Global Optim. 41, 135–145 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  10. Kinderlehrer, D., Stampacchia, G.: An Introduction to Variational Inequalities and Their Applications. Academic Press, New York (1980)

    MATH  Google Scholar 

  11. Muu, L.D., Quy, N.V.: On existence and solution methods for strongly pseudomonotone equilibrium problems. Vietnam J. Math. 43, 229–238 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  12. Pang, J.-S.: A posteriori error bounds for the linearly-constrained variational inequality problem. Math. Oper. Res. 12, 474–484 (1987)

    Article  MathSciNet  Google Scholar 

  13. Tam, N.N., Yao, J.C., Yen, N.D.: Solution methods for pseudomonotone variational inequalities. J. Optim. Theory Appl. 138, 253–273 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  14. Thanh Hao, N.: Tikhonov regularization algorithm for pseudomonotone variational inequalities. Acta Math. Vietnam. 31, 283–289 (2006)

    MathSciNet  MATH  Google Scholar 

  15. Yao, J.C.: Multivalued variational inequalities with K-pseudomonotone operator. J. Optim. Theory Appl. 83, 391–403 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  16. Zhu, D., Marcotte, P.: New classes of generalized monotonicity. J. Optim. Theory Appl. 87, 457–471 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  17. Verma, R.U.: Variational inequalities involving strongly pseudomonotone hemicontinuous mappings in nonreflexive Banach spaces. Appl. Math. Lett. 11, 41–43 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Acknowledgments

We would like to thank the referees for their constructive comments which significantly improve the presentation of the paper. The first author was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2013R1A1A2A10008908). The second author was supported by ICST HCMC and Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.01-2014.24. The third author was supported by the Vietnam Institute for Advanced Study in Mathematics (VIASM) and University of Pedagogy of Ho Chi Minh City.

Author information

Authors and Affiliations

  1. Department of Applied Mathematics, Pukyong National University, Pusan, 608-737, Republic of Korea

    Do Sang Kim

  2. Institute for Computational Science and Technology at Ho Chi Minh City (ICST HCMC), Ho Chi Minh City, Vietnam

    Phan Tu Vuong

  3. University of Technology and Education, Ho Chi Minh City, Vietnam

    Phan Tu Vuong

  4. Department of Mathematics, University of Pedagogy of Ho Chi Minh City, 280 An Duong Vuong, Ho Chi Minh City, Vietnam

    Pham Duy Khanh

Authors
  1. Do Sang Kim
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Phan Tu Vuong
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pham Duy Khanh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Do Sang Kim.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kim, D.S., Vuong, P.T. & Khanh, P.D. Qualitative properties of strongly pseudomonotone variational inequalities. Optim Lett 10, 1669–1679 (2016). https://doi.org/10.1007/s11590-015-0960-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11590-015-0960-x

Keywords

Search

Navigation