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Summary: Computational Mathematics and Mathematical Physics, Vol.40, No.9, 2000, pp. 12391254.
Translated from Zhurnal Vychislitel'noi Matematiki i Matematicheskoi Fiziki, Vol.40, No.9, 2000, pp. 12911307.
Original Russian Text Copyright c
#2000 by Antipin.
English Translation Copyright c
#2000 by MAIK Nauka/Interperiodika (Russia).
Solution Methods for Variational Inequalities
with Coupled Constraints
A.S. Antipin
Computing Center, Russian Academy of Sciences, ul. Vavilova 40, GSP-1, Moscow, 117967 Russia
Revised December 9, 2003
Variational inequalities with coupled constraints are considered. The class of sym-
metric vector functions that form coupled constraints is introduced. Explicit and implicit
prediction-type gradient and proximal methods are proposed for solving variational in-
equalities with coupled constraints. The convergence of the methods is proved.
1. STATEMENT OF THE PROBLEM
To solve a variational inequality with coupled constraints means to nd a vector v #
## 0
such that
#F (v # ), w - v # # # 0 #w
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