A filter-variable-metric method for nonsmooth convex constrained optimization

We propose an algorithm for solving nonsmooth convex constrained problems, which combines the ideas of the variable metric methods with the filter strategy for evaluating candidate points. The resulted algorithm inherits some attractive features from both approaches. On the one hand, the time-consuming quadratic programming sub-problems do not need to be solved. On the other hand, the dominance concept of multiobjective optimization was used and the new iterate must satisfy so-called filter criterion. Some encouraging preliminary computational results are reported.