Operator Splitting for a Homogeneous Embedding of the Linear Complementarity Problem

We present a first-order quadratic cone programming algorithm that can scale to very large problem sizes and produce modest accuracy solutions quickly. Our returns primal-dual optimal when available or certificates of infeasibility otherwise. It is derived by applying Douglas--Rachford splitting homogeneous embedding the linear complementarity problem, which general set membership includes programs (QCPs) as special case. Each iteration our procedure requires projecting onto convex solving system with fixed coefficient matrix. If sequence related problems are solved, then easily be warm-started make use factorization caching system. demonstrate on range public synthetic datasets for feasible approach tends somewhat faster than operator directly QCP, in cases significantly alternative approaches based diverging iterates. The we describe has been implemented C open-source solver SCS v3.0.