On bilevel variational inequalities arising in the analysis of improper optimization problems / Popov L.D. // Yugoslav Journal of Operations Research. - 2001. - V. 11, l. 1. - P. 3-14.

ISSN:
03540243
Type:
Article
Abstract:
A special class of bilevel monotone variational inequalities arising in the parametric analysis of monotone operator equations is investigated. Sufficient conditions for the existence of a solution are given and some numerical methods for these problems are proposed. Improper problems of mathematical programming, complementarity and game theory may be regarded as an area of application of the results of the theory and practice of ill-posed parametric systems of equations and convex inequalities.
Author keywords:
Improper optimization problems; Lexicographical variational inequalities; Monotone operators; Optimal correction of ill-posed instances; Stable solvability
Index keywords:
нет данных
DOI:
нет данных
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Affiliations Department of Mathematical Programming, Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation
Author Keywords Improper optimization problems; Lexicographical variational inequalities; Monotone operators; Optimal correction of ill-posed instances; Stable solvability
References Barushinski, A.B., Kokurin, M.Ju., Algorithm of iterative regularization for monotone variational inequalities (1999) Journal of Numerical Mathematics and Mathematical Physics, 4 (39), pp. 553-560. , in Russian; Brezis, H., Crandall, M.G., Paxy, A., Perturbations of nonlinear maximal monotone sets in Banach space (1970) Communications on Pure and Applied Mathematics, 23, pp. 123-144; Eremin, I.I., (1998) Contradictory Models of Optimal Planning, , Nauka, Moskow, in Russian; Eremin, I.I., Mazurov, V.D., Astafjev, N.N., (1983) Improper Problems of Linear and Convex Programming, , Nauka, Moskow, in Russian; Kalasnikov, V.V., Kalasnikova, N.I., Resolving bilevel variational inequalities (1994) Cybernetiks and System Analysis, 6, pp. 178-180. , in Russian; Kokurin, M.Ju., (1998) Operator Regularization and Investigation of Nonlinear Monotone Problems, , Joshkar-Ola: Marijsky State Univ., in Russian; Lavrntjev, M.M., Romanov, V.G., Shishatsky, S.P., (1980) Incorrect Problems of Mathematical Physics and Analysis, , Nauka, Moskow, in Russian; Minty, G.J., On a monotonicity method for the solution of nonlinear equations in Banach spaces (1963) Proceedings of the National Academy of Sciences of the USA, 50, pp. 1038-1041; Popov, L.D., Analysis of improper variational inequalities and monotone operator equations (1996) Informatic Bulletin of AMP, 6, pp. 46-57. , Ekaterinburg: UB RAS, in Russian; Popov, L.D., About the single-step method of resolving the lexicographical variational inequalities (1998) Izvestija Vuzov. Mathematics, 12, pp. 71-81. , in Russian; Rockafellar, R.T., On the maximality of sums of nonlinear monotone operators (1970) Transactions of the American Mathematical Society, 149, pp. 75-88; Skarin, V.D., About an approach to analysis of improper problems of linear programming (1986) Journal of Numerical Mathematics and Mathematical Physics, 26 (3), pp. 439-448. , in Russian; Tihonov, A.N., Arsenin, V.Ja., (1979) Resolution Methods for Incorrect Problems, , Nauka, Moskow, in Russian; Vainberg, M.M., (1972) Variation Methods and Methods of Monotone Operators, , Nauka, Moskow, in Russian
Correspondence Address Popov, L.D.; Department of Mathematical Programming, Institute of Mathematics and Mechanics, Ekaterinburg, Russian Federation
CODEN YJORE
Language of Original Document English
Abbreviated Source Title Yugosl J Oper Res
Source Scopus