GPU-accelerated Quadratic Conic Solvers

We introduce CuClarabel, a GPU-accelerated version of the interior-point solver Clarabel for quadratic cone programs. We describe the implementation through overviewing the homogeneous embedding method used in Clarabel and the mixed parallel computing strategy in CuClarabel. Compared to its CPU counterpart and other CPU-based solvers, the GPU solver demonstrates several times superior performance on various classes of problems, without compromising precision. Next, we survey backpropagation through convex problems leveraging differentiable cone programs, and showcase differentiating through quadratic cone programs. Through a blend of this work, we outline a forward path to efficient, GPU-accelerated differentiable convex optimization layers.