Outer approximation schemes for generalized semi-infinite variational inequality problems

Abstract

We introduce and analyse outer approximation schemes for solving variational inequality problems in which the constraint set is as in generalized semi-infinite programming. We call these problems generalized semi-infinite variational inequality problems. First, we establish convergence results of our method under standard boundedness assumptions. Second, we use suitable Tikhonov-like regularizations for establishing convergence in the unbounded case.

Keywords::

• variational inequalities
• maximal monotone operators; Banach spaces
• outer approximation algorithm
• generalized semi-infinite programs
• Bregman functions
• coercive operators

AMS Subject Classifications::

• 90C34
• 65K10
• 47J20
• 49J40

Acknowledgements

The authors are very grateful to the two referees for their helpful and valuable suggestions, which greatly improved an earlier version of the manuscript. R.S. Burachik acknowledges support by the Australian Research Council Discovery Project Grant DP0556685 for this study. The research of J.O. Lopes has been partially supported by AGIMP and CNPq.