Optimal distance method for Lagrangian multipliers updating in short-term hydro-thermal coordination

This paper deals with a novel Lagrangian multipliers correction procedure which is a significant and open question in all short-term hydro-thermal coordination procedures based on the Lagrangian relaxation technique. A new and original updating approach called the optimal distance method has been proposed. The basic idea of this method is to update Lagrangian multipliers trying to find the primal problem solution directly. The distance between the calculated dual solution and the optimal primal problem solution is computed and Lagrangian multipliers are updated in order to nullify that distance. Mathematically speaking, the optimal distance function is defined and its minimization is performed in the Lagrangian multipliers correction procedure. The method is based on Kuhn-Tucker optimality conditions which means that the minimization of the optimal distance function leads to satisfying all of these conditions. Performance of the proposed method are tested, analyzed and compared with results calculated using the subgradient technique.