A bundle method for hydrothermal scheduling

Lagrangian relaxation has been widely used in hydrothermal scheduling. Complicating constraints are relaxed by multipliers which are usually updated by a subgradient method (SGM). The SGM suffers from slow convergence caused by the nondifferentiable characteristics of dual functions. This paper presents an algorithm that utilizes the bundle trust region method (BTRM) to update the multipliers within the Lagrangian relaxation framework. The BTRM is shown to converge faster than the SGM as well as other bundle type methods in optimizing nondifferentiable dual functions. The application of BTRM for solving hydro subproblems results in greatly improved convergence over the SGM. Comparing BTRM with another bundle type method in updating the high level multipliers shows that better solution can be obtained by BTRM