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Multivalued Tikhonov Trajectories of General Affine Variational Inequalities

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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.

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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 

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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.

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Correspondence to N. D. Yen.

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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

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  • DOI: https://doi.org/10.1007/s10957-012-0226-z

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