Sensitivity Results in Optimization with Applications to Optimal Control Problems

For a general optimization problem we derive sensitivity results of the following type. We perturb parameters of the problem and give upper bounds for the optimal value of the perturbed problem. This leads to upper bounds for the directional derivatives of the value function. Our approach does not require normality or regularity assumptions about the solution of the original problem.

We apply these results to optimal control problems. First, we present results for a general problem with state or mixed constraints. Concluding, we show how in case of a singular optimal solution higher order necessary conditions may serve to improve the estimates obtained via first order conditions.