On dynamic optimization sensitivity analysis

This article describes a linear penalty method for getting sensitive information, i.e. the effect of variation on the constraint to the objective function. The dynamic optimization problem discussed here is a problem with state constraints. At first, the problem is formulated to unconstrained dynamic optimization problem by adding the constraints to the objective function as linear penalty terms. Then, the mathematical formulas to evaluate the change in the objective function and the optimal solution are derived if small perturbation introduced in the constraints. Lastly, the formulas are applied to some numerical examples. Comparison the result of numerical simulations to the numerical solutions obtained from reliable software, i.e. MISER 3.3, shows that the method in general is quite effective. The differences between two solutions are very small and insignificant.