Duality methods with an automatic choice of parameters Application to shallow water equations in conservative form

Summary.

In [3] a duality numerical algorithm for solving variational inequalities based on certain properties of the Yosida approximation of maximal monotone operators has been introduced. The performance of this algorithm strongly depends on the choice of two constant parameters. In this paper, we consider a new class of algorithms where these constant parameters are replaced by functions. We show that convergence properties are preserved and look for optimal values of these two functions. In general these optimal values cannot be computed, as they depend on the exact solution. Therefore, we propose some strategies in order to approximate them. The resulting algorithms are applied to three variational inequalities in order to compare their performance with that of the original algorithm.