In this talk, we present a method for identifying infeasible, unbounded, and pathological conic programs based on Douglas-Rachford splitting, or equivalently ADMM. When an optimization program is infeasible, unbounded, or pathological, the iterates of Douglas-Rachford splitting diverge. Somewhat surprisingly, such divergent iterates still provide useful information, which our method uses for identification. As a first-order method, the proposed algorithm relies on simple subroutines and therefore is simple to implement and has low per-iteration cost.

This is joint work with Yanli Liu and Ernest Ryu.