This paper presents an algorithm for optimization of large scale non-linear dynamical problems with linear constraints. The approach was devised with the aim of solving deterministic scheduling problems of hydrothermal power systems. The method has a conception based on the overall structure of the reduced gradient method, more specifically it is based on the implementation of this method by Murtagh and Saunders (1978). The dynamical characteristic of the problem leads to a constraints matrix with staircase structure. Skillfulluse of this feature in storing and computations is mandatory for large scale problems. The staircase structure is considered in the L-U decomposition of the constraints matrix and in the updatong scheme which is based in the classic paper of Bartels-Golub. The algorithm was implemented in a computer program and a application to load scheduling is presented.
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