Applied Mathematics and Optimization

, Volume 57, Issue 1, pp 125–147

Hölder Continuity of Adjoint States and Optimal Controls for State Constrained Problems


DOI: 10.1007/s00245-007-9015-8

Cite this article as:
Bettiol, P. & Frankowska, H. Appl Math Optim (2008) 57: 125. doi:10.1007/s00245-007-9015-8


We investigate Hölder regularity of adjoint states and optimal controls for a Bolza problem under state constraints. We start by considering any optimal solution satisfying the constrained maximum principle in its normal form and we show that whenever the associated Hamiltonian function is smooth enough and has some monotonicity properties in the directions normal to the constraints, then both the adjoint state and optimal trajectory enjoy Hölder type regularity. More precisely, we prove that if the state constraints are smooth, then the adjoint state and the derivative of the optimal trajectory are Hölder continuous, while they have the two sided lower Hölder continuity property for less regular constraints. Finally, we provide sufficient conditions for Hölder type regularity of optimal controls.


Bolza optimal control problemState constraintsMaximum principleSmooth minimizersHölder optimal controls

Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.SISSA/ISASTriesteItaly
  2. 2.CNRS, CREAEcole PolytechniqueParisFrance