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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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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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