On some continuity properties of the measure lagrange multiplier from the maximum principle for state constrained problems

The continuity of the Lagrange multiplier μ(t) from the maximum principle for control problems with state constraints is investigated. It is proved, under certain regularity assumptions, that the function μ(t) is Hölder continuous with exponent 1/2. Under regularity conditions plus the strong Legendre condition, this function is Lipschitz continuous. © 2015 Society for Industrial and Applied Mathematics.