Abstract
The weak ordering is generalized in Banach spaces; Vector Complementarity Systems and Vector Variational Inequalities are introduced based on this new ordering, and relations are discussed between them.
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References
Bianchi M., Hadjisavvas N. and Schaible S., “Vector equilibrium problems with generalized monotone bifunctions”. Jou. of Optimiz. Theory and Appls., V. 92, 1997, pp. 531–546.
Chen G-Y. and Yang X-Q., “The vector complementarity problem and its equivalences with the weak minimal element in ordered spaces”. Jou. of Mathem. Analysis and Appls., V. 153, 1990, pp. 136–158.
Cottle R.W., Giannessi F. and Lions J-L., (eds.), “Variational inequalities and complementarity problems”. John Wiley and Sons, Chichester, New York, Brisbane, Toronto, 1980.
Daniilidis A. and Hadjisavvas N., “Existence theorems for vector variational inequalities”. Bull. of the Australian Mathem. Soc., V. 54, 1996, pp. 473–481.
Giannessi F., “Theorems of alternative, quadratic programs and complementarity problems”. In [3], pp.151–186.
Giannessi F., “Theorems of the alternative and optimality conditions”. Jou. of Optimiz. Theory and Appls., V. 42, 1984, pp. 331–365.
Giannessi F., “On Minty variational principle”. In: “New trends in mathematical programming”, Giannessi F., Komlósi S. and Rapcsâk T. (eds.), Kluwer Academic Publishers, Boston, Dordrecht, London, 1998, pp. 93–99.
Giannessi F. and Rapcsak T., “Images, separation of sets and extremum problems”. In: “Recent trends in optimization theory and Appls.”, Agarwal R.P. (ed.), World Scientific, World Scientific Series in Applicable Analysis, V.5, Singapore, New Jersey, London, Hong Kong, 1998, pp. 79–106.
Lee B.S., Lee G.M. and Kim D.S., “Generalized vector variational-like inequalities on locally convex Hausdorff topologiacal vector spaces”. Indian Jou. of Pure Appl. Mathem., V. 28, 1997, pp. 3341.
Oettli W. and Schläger D., “Generalized vectorial equilibria and generalized monotonicity”. In: “Functional analysis with current applications in science, technology and industry”, Brokate M. and Siddiqi A.H. (eds.), Pitman Research Notes in Mathematics, Nr. 377, Longman, Harlow, 1998, pp. 145–154.
Yang X.Q., “Vector complementarity and minimal element problem”. Jou. of Optimiz. Theory and Appls., V.77, 1993, pp.483–495.
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Rapcsák, T. (2000). On Vector Complementarity Systems and Vector Variational Inequalities. In: Giannessi, F. (eds) Vector Variational Inequalities and Vector Equilibria. Nonconvex Optimization and Its Applications, vol 38. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-0299-5_22
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DOI: https://doi.org/10.1007/978-1-4613-0299-5_22
Publisher Name: Springer, Boston, MA
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Online ISBN: 978-1-4613-0299-5
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