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Extra resources for Optimal Inventory Mode of Systems Multi Echelon Techniques
Sample text
The fourth order Runge-Kutta method [30, 1965] (a standard method for solving ordinary differential equations) is slightly modified for solving a differential equation of the form where is a step-function. The modification is simply recording the counting number and time to make sure that always takes the appropriate value not in subinterval when In the computation, the differential equation is computed forward (starting at while the adjoint equation is solved backward (starting at Two steps are introduced to solve such optimal control problems: 1 Compute objective values from the objective function, differential equation, and augmented Lagrangian, not compute gradients from the adjoint equation and Hamiltonian.
The limitations of the above computational approaches are summarized in Chen and Craven [10, 2002]. From the above survey it will also appear that each of the above computational methods has characteristics which are computationally efficient for computing optimal control financial models with switching times. A new approach which can adapt various convenient components of the above computational approaches is developed in the next section. Although the present algorithm has similarity with CPET, the details of the two algorithms are different.
Jumping between two levels. This kind of control patterns is also considered in this research. Øksendal [3, 1991]. Mundaca and Øksendal [62, 1998] and Cadenillas and Zapatero [6, 2000] work on the applications to the control of currency exchange rates. 7 CPET Time optimal control problems (which are not considered in this research) with bang-bang control associated with or without singular arc solutions can make the calculation difficult. A novel problem transformation called the Control Parameterization Enhancing Transform (CPET) was introduced in reference [51, 1997] to provide a computationally simple and numerically accurate solution without assuming that the optimal control is pure bang-bang control for time optimal control problems.