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A von Neumann Alternating Method for Finding Common Solutions to Variational Inequalities

Yair Censor(yair***at***math.haifa.ac.il)
Aviv Gibali(avivg***at***techunix.technion.ac.il)
Simeon Reich(sreich***at***techunix.technion.ac.il)

Abstract: Modifying von Neumann's alternating projections algorithm, we obtain an alternating method for solving the recently introduced Common Solutions to Variational Inequalities Problem (CSVIP). For simplicity, we mainly confine our attention to the two-set CSVIP, which entails finding common solutions to two unrelated variational inequalities in Hilbert space.

Keywords: Alternating method, averaged operator, fixed point, Hilbert space, inverse strongly monotone operator, metric projection, nonexpansive operator, resolvent, variational inequality.

Category 1: Complementarity and Variational Inequalities

Category 2: Nonlinear Optimization

Citation: Nonlinear Analysis Series A: Theory, Methods & Applications, accepted for publication.

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Entry Submitted: 02/03/2012
Entry Accepted: 02/03/2012
Entry Last Modified: 02/03/2012

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