Multivalued Tikhonov Trajectories of General Affine Variational Inequalities (original) (raw)

Abstract

The Tikhonov trajectory of a general, not necessarily monotone, affine variational inequality is analyzed via the basic properties like single-valuedness, finite-valuedness, continuity, and convergence. We study the multivalued trajectory, which is obtained, by the Tikhonov regularization method, on the whole interval of positive parameters.

Access this article

Log in via an institution

Subscribe and save

• Starting from 10 chapters or articles per month
• Access and download chapters and articles from more than 300k books and 2,500 journals
• Cancel anytime View plans

Buy Now

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

Instant access to the full article PDF.

Similar content being viewed by others

References

1. Gowda, M.S., Pang, J.-S.: On the boundedness and stability of solutions to the affine variational inequality problem. SIAM J. Control Optim. 32, 421–441 (1994)
   Article MathSciNet MATH Google Scholar
2. Lee, G.M., Tam, N.N., Yen, N.D.: Quadratic Programming and Affine Variational Inequalities: a Qualitative Study. Springer, New York (2005)
   Google Scholar
3. Cottle, R.W., Pang, J.-S., Stone, R.E.: The Linear Complementarity Problem. Academic Press, New York (1992)
   MATH Google Scholar
4. Facchinei, F., Pang, J.-S.: Finite-Dimensional Variational Inequalities and Complementarity Problems, vols. I and II. Springer, New York (2003)
   Google Scholar
5. Khanh, P.D.: On the Tikhonov regularization of affine pseudomonotone mappings. Optim. Lett. (to appear)
6. Huong, N.T.T., Hoa, T.N., Phuong, T.D., Yen, N.D.: A property of bicriteria affine vector variational inequalities. Appl. Anal. (2012). doi:10.1080/00036811.2011.649732 (Online First)
   MathSciNet Google Scholar
7. Thanh Hao, N.: Tikhonov regularization algorithm for pseudomonotone variational inequalities. Acta Math. Vietnam. 31, 283–289 (2006)
   MathSciNet MATH Google Scholar
8. 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
9. Yao, J.-C., Chadli, O.: Pseudomonotone complementarity problems and variational inequalities. In: Hadjisavvas, N., Komlósi, S., Schaible, S. (eds.) Handbook of Generalized Convexity and Generalized Monotonicity, pp. 501–558. Springer, New York (2005)
   Chapter Google Scholar

Download references

Acknowledgements

The research of the authors is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant number 101.02-2011.01. The first, the second, and the third authors were supported in part respectively by Department of Information Technology, Le Qui Don University, by University of Pedagogy of Ho Chi Minh City, and by the International Centre for Theoretical Physics, Trieste, Italy. We are indebted to Professor Franco Giannessi and the anonymous referee for very helpful comments and suggestions.

Author information

Authors and Affiliations

1. Department of Information Technology, Le Qui Don University, 100 Hoang Quoc Viet, Hanoi, Vietnam
   N. T. T. Huong
2. Department of Mathematics, University of Pedagogy of Ho Chi Minh City, 280 An Duong Vuong, Ho Chi Minh, Vietnam
   P. D. Khanh
3. Institute of Mathematics, Vietnam Academy of Science and Technology, 18 Hoang Quoc Viet, Hanoi, 10307, Vietnam
   N. D. Yen

Authors

1. N. T. T. Huong
2. P. D. Khanh
3. N. D. Yen

Corresponding author

Correspondence toN. D. Yen.

Rights and permissions

About this article

Cite this article

Huong, N.T.T., Khanh, P.D. & Yen, N.D. Multivalued Tikhonov Trajectories of General Affine Variational Inequalities.J Optim Theory Appl 158, 85–96 (2013). https://doi.org/10.1007/s10957-012-0226-z

Download citation

• Received: 16 February 2012
• Accepted: 12 November 2012
• Published: 22 November 2012
• Issue date: July 2013
• DOI: https://doi.org/10.1007/s10957-012-0226-z

Keywords