  DC Optimal Power Flow (DCOPF) is a key operational tool for power system
operators, and it is embedded as a subproblem in many challenging optimization
problems (e.g., line switching). However, traditional CPU-based solve routines
(e.g., simplex) have saturated in speed and are hard to parallelize. This paper
focuses on solving DCOPF problems using gradient-based routines on Graphics
Processing Units (GPUs), which have massive parallelization capability. To
formulate these problems, we pose a Lagrange dual associated with DCOPF (linear
and quadratic cost curves), and then we explicitly solve the inner (primal)
minimization problem with a dual norm. The resulting dual problem can be
efficiently iterated using projected gradient ascent. After solving the dual
problem on both CPUs and GPUs to find tight lower bounds, we benchmark against
Gurobi and MOSEK, comparing convergence speed and tightness on the IEEE 2000
and 10000 bus systems. We provide reliable and tight lower bounds for these
problems with, at best, 5.4x speedup over a conventional solver.
