  This paper is an attempt to remedy the problem of slow convergence for
first-order numerical algorithms by proposing an adaptive conditioning
heuristic. First, we propose a parallelizable numerical algorithm that is
capable of solving large-scale conic optimization problems on distributed
platforms such as {graphics processing unit} with orders-of-magnitude time
improvement. Proof of global convergence is provided for the proposed
algorithm. We argue that on the contrary to common belief, the condition number
of the data matrix is not a reliable predictor of convergence speed. In light
of this observation, an adaptive conditioning heuristic is proposed which
enables higher accuracy compared to other first-order numerical algorithms.
Numerical experiments on a wide range of large-scale linear programming and
second-order cone programming problems demonstrate the scalability and
computational advantages of the proposed algorithm compared to commercial and
open-source state-of-the-art solvers.
