An explicit algorithm for monotone variational inequalities

Abstract

We introduce a fully explicit method for solving monotone variational inequalities in Hilbert spaces, where orthogonal projections onto the feasible set are replaced by projections onto suitable hyperplanes. We prove weak convergence of the whole generated sequence to a solution of the problem, under only the assumptions of continuity and monotonicity of the operator and existence of solutions.

Keywords:

• maximal monotone operators
• monotone variational inequalities
• projection method
• relaxed method
• weak convergence

AMS Subject Classifications:

• 90C47
• 49J35

Acknowledgements

J.Y. Bello Cruz was partially supported by PROCAD UFG/UnB/IMPA. A.N. Iusem was partially supported by CNPq grant No. 301280-86.