New decomposition and convexification algorithm for nonconvex large-scale primal-dual optimization

A new algorithm for solving nonconvex, equality-constrained optimization problems with separable structures is proposed in the present paper. A new augmented Lagrangian function is derived, and an iterative method is presented. The new proposed Lagrangian function preserves separability when the original problem is separable, and the property of linear convergence of the new algorithm is also presented. Unlike earlier algorithms for nonconvex decomposition, the convergence ratio for this method can be made arbitrarily small. Furthermore, it is feasible to extend this method to algorithms suited for inequality-constrained optimization problems. An example is included to illustrate the method.This research was supported in part by the National Science Foundation under NSF Grant No. ECS-85-06249.