Abstract
In this study, we discuss one type of variational inequality problem with a fuzzy convex cone \(\tilde X\), denoted by VI(\(\tilde X\), f). Different classes of fuzzy convex cones which are considered in different context of the problems will be discussed. According to the existence theorem, an approach derived from the concepts of multiple objective mathematical programming problems for solving the VI(\(\tilde X\), f) is proposed. An algorithm is developed to find its fuzzy optimal solution set with complexity analysis.
Similar content being viewed by others
References
Giannessi, F. and Maugeri, A. (1995), Variational Inequalities and Equilibrium Network Problems, Plenum Press, New York.
Harker, P.T. and Pang, J.S. (1990), Finite-dimensional variational inequality and nonlinear complementarity problems: a survey of theory, algorithms and applications, Mathematical Programming 48: 161-220.
Kinderlehrer, D. and Stampacchia, G. (1980), An Introduction to Variational Inequalities and Their Applications, Academic Press, New York.
Klir, G.J. and Folger, T.A. (1988), Fuzzy Sets, Uncertainty, and Information, Prentice-Hall, New Jersey.
Liebman, J. et al. (1986), Modeling and Optimization with GINO, The Scientific Press Publisher.
Noar, M.A. (1996), Computational techniques for variational inequalities, Journal of Natural Geometry 9: 41-62.
Noar, M.A., Noar, K.I. and Rassias, Th.M. (1993), Some aspects of variational inequalities, Journal of Computational Applied Mathematics 47: 285-312.
Wang, H.F. and Liao, H.L. Resolution of the variational inequality problems, submitted to Journal of Optimization Theory and Application.
Wang, H.F. and Liao, H.L. (1996), Variational inequality with Fuzzy function, The Journal of Fuzzy Mathematics 4: 149-169.
Zimmermann, H.J. (1988), Fuzzy Set Theory and its Applications, 3rd edn., Kluwer/Nijhoff, Boston.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Wang, HF., Liao, HL. Variational Inequality with Fuzzy Convex Cone. Journal of Global Optimization 14, 395–414 (1999). https://doi.org/10.1023/A:1008217225099
Issue Date:
DOI: https://doi.org/10.1023/A:1008217225099