Popular approach to solving NUM utilizes dual decomposition and subgradient iterations, which are extremely slow to converge. Recently there has been investigation of barrier methods for the solution of NUM which have been shown to possess second order convergence. However, the question of accelerating dual decomposition based methods is still open. We propose a novel semismooth equation approach to solving the standard dual decomposition formulation of NUM. We show that under fairly mild assumptions that the approach converges locally superlinearly to the solution of the NUM. Globalization of the proposed algorithm using a linesearch is also described. Numerical experiments show that the approach is competitive with a state-of-the-art nonlinear programming solver which solves the NUM without decomposition.