Superlinear rate of convergence and optimal acceleration schemes in the solution of convex inequality problems. (Q2768022)

The convergence rate of projection techniques for the convex inequality problem is a very important issue. Therefore, much effort is being spent on acceleration schemes to achieve guaranteed better convergence. The paper proves the existence of a scheme that has a superlinear convergence rate. It is shown that it can be achieved by solving the dual of a quadratic problem that finds the projection of a point on a group of violated and almost violated constraints. Some hints are also given for the possible implementations of the method. Computational experiences are not reported.NEWLINENEWLINEFor the entire collection see [Zbl 0971.00058].