Skip to main content
Springer Nature Link
Log in

A descent method for mixed variational inequalities

  • Published:
Journal of Systems Science and Complexity Aims and scope Submit manuscript

Abstract

A new descent method for solving mixed variational inequalities is developed based on the auxiliary principle problem. Convergence of the proposed method is also demonstrated.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
€32.70 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (France)

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cohen G, Optimization by decomposition and coordination: A unified approach, IEEE Transactions on Automatic Control, 1978, 23(2): 222–4.

    Article  MATH  Google Scholar 

  2. Cohen G, Auxiliary problem principle and decomposition of optimization problems, Journal of Optimization Theory and Application, 1980, 32(3): 277–4.

    Article  MATH  Google Scholar 

  3. Cohen G and Zhu D L, Decomposition coordination method in large-scale optimization problems: The nondierentiable case and the use of augmented lagrangians, Advances in Large-Scale Systems: Theory and Applications, Ed. by Cruz J B, JAI Press, Greenwich, Connecticut, 1984, 1: 203–3.

    MathSciNet  Google Scholar 

  4. Cohen G, Auxiliary problem principle extended to variational inequalities, Journal of Optimization Theory and Application, 1988, 59(2): 325–4.

    MATH  Google Scholar 

  5. Zhu D L and Marcotte P, Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities, SIAM Journal of Optimization, 1996, 6(3): 714–4.

    Article  MATH  MathSciNet  Google Scholar 

  6. Verma R U, Generalized auxiliary problem principle and solvability of a class of nonlinear variational inequalities involving cocoercive and co-lipschitzian mappings, Journal of Inequalities in Pure and Applied Mathematics, 2001, 2(3), article 27.

    MathSciNet  Google Scholar 

  7. Stampacchia G, Formes bilineaires coercitives sur les ensembles convexes, C. R. Acad. Sci. Paris, 1964, 258: 4413–3 (French).

    MATH  MathSciNet  Google Scholar 

  8. Facchinei F and Pang J S, Finite-Dimensional Variational Inequalities and Complementarity Problems, Vols. 1 and 2, Springer, New Yourk, 2003.

    Google Scholar 

  9. Noor M A, A new iterative method for mixed variational inequalities, Mathematical and Computer Modelling, 1997, 26(7): 29–4.

    Article  MATH  MathSciNet  Google Scholar 

  10. Noor M A, Numerical methods for mixed variational inequalities, Advance Nonlinear Variational Inequalities, 1998, 1: 51–3.

    MATH  Google Scholar 

  11. Noor M A, An extraresolvent method for monotone mixed variational inequalities, Mathematical and Computer Modelling, 1999, 29(3): 95–4.

    Article  MATH  MathSciNet  Google Scholar 

  12. Konnov I V, Combined Relaxation Methods for Variational Inequalities, Spring-Verlag, Berlin, 2001.

    Google Scholar 

  13. Xiu N H, Wang Y J, and Zhang X S, Modified fixed-point equations and related iterative method for variational inequalities, Computers and Mathematics with Applications, 2004, 47(6–7): 913–2.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Management, Shandong University, Jinan, 250100, China

    Jianghua Zhang

  2. School of International Trade and Economics, University of International Business and Economics, Beijing, 100029, China

    Yingxue Zhao

  3. Institute of Systems Science, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Shouyang Wang

Authors
  1. Jianghua Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yingxue Zhao
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Shouyang Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yingxue Zhao.

Additional information

This work was partially supported by the National Natural Science Foundation of China under Grant No. 71201093, the Research Fund for Doctoral Program of Ministry of Education of China under Grant No. 20120131120084, the Promotive Research Fund for Excellent Young and Middle-aged Scientists of Shandong Province under Grant No. BS2012SF012, and the Independent Innovation Foundation of Shandong University under Grant No. IFYT14011.

This paper was recommended for publication by Editor ZHANG Xun.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhang, J., Zhao, Y. & Wang, S. A descent method for mixed variational inequalities. J Syst Sci Complex 28, 1307–1311 (2015). https://doi.org/10.1007/s11424-015-3036-1

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11424-015-3036-1

Keywords

Search

Navigation