  This paper offers a matrix-free first-order numerical method to solve
large-scale conic optimization problems. Solving systems of linear equations
pose the most computationally challenging part in both first-order and
second-order numerical algorithms. Existing direct and indirect methods are
either computationally expensive or compromise on solution accuracy.
Alternatively, we propose an easy-to-compute decomposition method to solve
sparse linear systems that arise in conic optimization problems. Its iterations
are tractable, highly parallelizable, with closed-form solutions. This
algorithm can be easily implemented on distributed platforms, such as graphics
processing units, with orders-of-magnitude time improvement. The performance of
the proposed solver is demonstrated on large-scale conic optimization problems
and is compared with the state-of-the-art first-order solvers.
