TITLE: Splitting Methods for Conic Programs including Their Pathological Cases

ABSTRACT:

First-order methods such as ADMM and Douglas-Rachford splitting are known for their easy implementations and low per-iteration costs. What is less known is their usefulness for developing parallel algorithms for solving certain conic programs including both well-behaved and pathological (infeasible or feasible-but-unbounded) instances. In the first part of this talk, we present an algorithm and its software implementation under development for solving LPs and SOCPs using parallel and distributed computing.  In the second part, we present a method for classifying infeasible, unbounded, and other pathological conic programs based on a divergent sequence of Douglas-Rachford splitting. Our method can identify some of the weakly infeasible and weakly unbounded cases that existing interior-point solvers cannot do reliably.

BIO:  Wotao Yin
Affiliation: University of California; Los Angeles