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Extensions of Korpelevich’s extragradient method for the variational inequality problem in Euclidean space. (English) Zbl 1260.65056
Summary: We present two extensions of Korpelevich’s extragradient method for solving the variational inequality problem (VIP) in the Euclidean space. In the first extension, we replace the second orthogonal projection onto the feasible set of the VIP in Korpelevich’s extragradient method with a specific subgradient projection. The second extension allows projections onto the members of an infinite sequence of subsets which epi-converges to the feasible set of the VIP. We show that in both extensions the convergence of the method is preserved and present directions for further research.
MSC:
65K10Optimization techniques (numerical methods)
49K10Free problems in several independent variables (optimality conditions)