Article ID: | iaor2013263 |
Volume: | 7 |
Issue: | 1 |
Start Page Number: | 185 |
End Page Number: | 206 |
Publication Date: | Jan 2013 |
Journal: | Optimization Letters |
Authors: | Chbani Zaki, Riahi Hassan |
Keywords: | programming (minimax), Ky Fan inequality |
In this paper we present the relaxed inertial proximal algorithm for Ky Fan minimax inequalities. Based on Opial lemma, we propose a weak convergence result to a solution of the problem by eliminating in the algorithm (RIPAFAN) the Browder–Halpern’s factor of contraction. We present after, a first result of strong convergence by adding a strong monotonicity condition. Secondly, we eliminate the strong monotonicity and add a Browder–Halpern’s contraction factor in the algorithm (RIPAFAN) and then ensure the strong convergence to a selected solution with respect to the contraction factor. Some examples are proposed. The first one concerns the convex minimization where the objective function is only controlled with a provided well conditioning. In the second one, we propose monotone set‐valued variational inequalities. The last example deals with the problem of fixed point for a nonexpansive set‐valued operator.