This paper considers the problem of optinal operation of hydro-thermal electric power systems. A system with a general configuration of multi-chains of reservoirs hydro sybsystem is treated. Optimal operation strategies developed using the minimum norm problem formulation of functional analytic optimization are given. The computational aspects of actually inplementing the strategies are discussed. In particular a general modified contraction mapping algorithm is treated. Computational experiments with a number of algorithms are reported for a sample system. Convergence characteristics of each algorithm are discussed.