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METHOD FOR SOLVING VARIATION INEQUALITIES USING INACCURATE INITIAL DATA
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METHOD FOR SOLVING VARIATION INEQUALITIES USING INACCURATE INITIAL DATA
Annotation
PII
S042473880000616-6-1
Publication type
Article
Status
Published
Authors
Evgeny Golshtein 
Edition
Issue №3
Pages
117-127
Abstract
The connection between solving variational inequality and finding the fixed element of the point to set mapping from convex compact to itself is established. Examples of variational inequalities relating to the convex optimization, convex antagonistic game, convex many person non-coalition game, the problem to find equilibrium prices are given. We describe an iterative method of the Oracle type for solving variational inequality defined by the monotone mapping under Oracle mistakes. We set the requirement to Oracle mistakes which guarantee to find ε-solution to variation inequality (with given ε > 0). The upper-bound for number of iterations necessary for calculating ε-solution to variation inequality is obtained.
Date of publication
01.07.2008
Number of purchasers
2
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785
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Behr K., Gol'shtejn E.G., Sokolov N.A. (2000): Ob ispol'zovanii metoda urovnej dlya minimizatsii vypuklykh funktsij, ne vse znacheniya kotorykh konechny // Ehkonomika i mat. metody. T. 36. № 4.
 Gol'shtejn E.G. (2002): Metod resheniya variatsionnykh neravenstv, opredelyaemykh monotonnymi otobrazheniyami // Zhurnal vychislitel'noj mat. i mat. fiziki. T. 42. № 7.
 Gol'shtejn E.G., Tret'yakov N.V. (1989): Modifitsirovannye funktsii Lagranzha. Teoriya i metody optimizatsii. M.: Fizmatlit.
 Mityushin L.G., Polterovich V.M. (1978): Kriterij monotonnosti funktsij sprosa // Ehkonomika i mat. metody. T. 14. № 1.
 Brower L.E.J. (1909): On Continuous Vector Distributions of Surfaces // Amsterdam Proc. Vol. 11. Continued in 1910. Vol. 12, 13.
 Kakutani S. (1941): A Generalization of Brower’s Fixed Point Theorem // Duke Math J. Vol. 8. № 3.

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