Weighted variational inequalities in non-pivot Hilbert spaces with applications

Authors:
Annamaria Barbagallo;Stéphane Pia
Affiliations:
Department of Mathematics and Computer Science, University of Catania, Catania, Italy 95125;Department of Mathematics and Computer Science, University of Catania, Catania, Italy 95125
Venue:
Computational Optimization and Applications
Year:
2011

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Abstract

We introduce variational inequalities defined in non-pivot Hilbert spaces and we show some existence results. Then, we prove regularity results for weighted variational inequalities in non-pivot Hilbert space. These results have been applied to the weighted traffic equilibrium problem. The continuity of the traffic equilibrium solution allows us to present a numerical method to solve the weighted variational inequality that expresses the problem. In particular, we extend the Solodov-Svaiter algorithm to the variational inequalities defined in finite-dimensional non-pivot Hilbert spaces. Then, by means of a interpolation, we construct the solution of the weighted variational inequality defined in a infinite-dimensional space. Moreover, we present a convergence analysis of the method.