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A new extragradient method for generalized variational inequality in Euclidean space. (English) Zbl 1303.90105

Summary: In this paper, we extend the extragradient projection method proposed in [Y. J. Wang et al., J. Optimization Theory Appl. 119, No. 1, 167–183 (2003; Zbl 1045.49017)] for the classical variational inequalities to the generalized variational inequalities. For this algorithm, we first prove its expansion property of the generated sequence with respect to the starting point and then show that the existence of the solution to the problem can be verified through the behavior of the generated sequence. The global convergence of the method is also established under mild conditions.

MSC:

90C33 Complementarity and equilibrium problems and variational inequalities (finite dimensions) (aspects of mathematical programming)
15A06 Linear equations (linear algebraic aspects)
90C30 Nonlinear programming

Citations:

Zbl 1045.49017
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References:

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