New Decomposition and Convexification Methods for Nonconvex Large-Scale Primal-Dual Optimization

In this short paper, we propose a new augumented Lagrangian function for the nonconvex equality-constrained optimization problem, and present an iterative method for solving it. If the problem is separable, then so is the proposed Lagrangian function and the iterative method may take advantage of decomposition. Unlike the earlier methods for nonconvex decomposition, the ratio of convergence for this method can be made arbitrarily small.