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In the paper the optimization problems which may be solved by the direct decomposition method are considered. It is possible when the performance index is a monotone function of other performance indices, which depend on two subsets of decision variables: an individual for every inner performance index and a common one for all. In the paper both the underlying theory and the basic numerical techniques are presented and compared. A special attention is paid to the guarantees of convergence in different classes of problems and to the expected effectiveness of calculations.

In the paper, a problem of dynamic optimal portfolio selection is considered. We examine an approach with two criteria: expected value and variance. The main difficulty is of that the variance criterion is not separable in time, even for the cost (benefit) function of Bolza type. Two methods of determining optimal control with expected value-variance criteria are tested: method based on the Lagrange function (finite time horizon) and method based on the linear programming (infinite time horizon). These methods were applied to a problem of investing in assets at the main market of the Warsaw stock-exchange.

The paper is devoted to a general nonlinear regulator design problem. In this context some connections between discrete version of the receding horizon control problem and the generalized network routing problem are considered. Except “standard” definition of the Lyapunov function with the help of the Bellman optimal cost-to-go function, it is shown, that the optimizing mapping corresponds to the Bellman-Ford routing algorithm. As such, it can be implemented asynchronously, e.g. in a Hopfield type neural network. The obtained routing tables will be control rules of an optimal receding horizon regulator. At the end some results of the application of this approach to an inverted pendulum control problem are presented.