SIAM Journal on Control and Optimization, Vol.53, No.4, 2514-2540, 2015
ON SOME CONTINUITY PROPERTIES OF THE MEASURE LAGRANGE MULTIPLIER FROM THE MAXIMUM PRINCIPLE FOR STATE CONSTRAINED PROBLEMS
The continuity of the Lagrange multiplier mu(t) from the maximum principle for control problems with state constraints is investigated. It is proved, under certain regularity assumptions, that the function mu(t) is Holder continuous with exponent 1/2. Under regularity conditions plus the strong Legendre condition, this function is Lipschitz continuous.