An extragradient-type algorithm for non-smooth variational inequalities
Alfredo Noel Iusem, L. R. Lucambio Pérez · Optimization · 2000
In this paper we study extragradient-type methods to solve variational inequality problems involving maximal monotone point-to-set operators. We will show, using an example, that, in this case, to achieve convergence to the solution set of sequences generated by extragradient methods it is necessary, in the search of the auxiliary point and its suitable image by the involved operator, to enlarge the set of possible search directions. Such an enlargement, a generalization of the ε-subgradient, is known and we use it to overcome this failure of the extragradient-methods. We propose a new algo-rithm and prove that it generates a sequence convergent to a solution point of the problem also when the operator is point-to-set