Elements of Numerical Mathematical Economics with Excel

10.11. Steepest descent numerical approach for optimal control problems using VBA

The procedure to solve an optimal control problem via the numerical technique of the steepest descent method goes through the following basic steps.

• 1. Simulate an approximate control variable path as initial guess, denoted by u ⁽⁰⁾ (t), over the time interval [t _0, T] and store it in the Excel worksheet.
• 2. We will see the following two cases:
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  Table 10.10-4

  Example 2: inventory problem constrained solution.

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  Figure 10.10-7 Example ...