Range of the displacement operator of PDHG with applications to quadratic and conic programming

Primal-dual hybrid gradient (PDHG) is a first-order method for saddle-point problems and convex programming introduced by Chambolle and Pock. Recently, Applegate et al. analyzed the behavior of PDHG when applied to an infeasible or unbounded instance of linear programming, and in particular, showed that PDHG is able to diagnose these conditions. Their analysis hinges on … Read more

Limits of eventual families of sets with application to algorithms for the common fixed point problem

We present an abstract framework for asymptotic analysis of convergence based on the notions of eventual families of sets that we define. A family of subsets of a given set is called here an “eventual family” if it is upper hereditary with respect to inclusion. We define accumulation points of eventual families in a Hausdorff … Read more