Latest experiences in improving convergence of dual optimization in LR method

This paper presents latest application experiences in dual optimization performance in Lagrangian relaxation (LR) method for solving power system resource scheduling problems. LR is widely used in solving a common class of optimization problems where the removal of the coupling constraints results in a collection of subproblems that can be independently and efficiently solved. The overall efficiency of the LR method is predominately determined by the computational efficiency of the dual optimization procedure, i.e. the number of iterations and the computational effort in each iteration. Although several alternatives have been developed, most of which can achieve eventual convergence in theory, no solution approach has been found to produce consistent and satisfactory convergence performance in practice. The most common approach for dual problem optimization, the subgradient method, used by many practitioners for its simplicity and low computational overhead, has been reported to suffer from slow convergence or premature stall. This paper presents encouraging experiences in achieving speedy convergence by judicious determination of the step size scaling factor based on simple rules that can be easily codified.