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- Title
Weighted variational inequalities in non-pivot Hilbert spaces with applications.
- Authors
Barbagallo, Annamaria; Pia, Stéphane
- 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.
- Subjects
VARIATIONAL inequalities (Mathematics); HILBERT space; NUMERICAL analysis; INTERPOLATION; STOCHASTIC convergence
- Publication
Computational Optimization & Applications, 2011, Vol 48, Issue 3, p487
- ISSN
0926-6003
- Publication type
Article
- DOI
10.1007/s10589-009-9259-0