On Some Continuity Properties of the Measure Lagrange Multiplier from the Maximum Principle for State Constrained Problems
Aram Vladimirovich Arutyunov, Dmitry Yu. Karamzin · SIAM Journal on Control and Optimization · 2015
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 Hölder continuous with exponent 1/2. Under regularity conditions plus the strong Legendre condition, this function is Lipschitz continuous.