optimal control second-order necessary optimality conditions second-order tangents
Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 39, No 3-4, (2013), 233p-270p
A second-order variational inclusion for control systems under state constraints is derived and applied to investigate necessary optimality conditions for the Mayer optimal control problem. A new pointwise condition verified by the adjoint state of the maximum principle is obtained as well as a second-order necessary optimality condition in the integral form. Finally, a new sufficient condition for normality of the maximum principle is proposed. Some extensions to the Mayer optimization problem involving a differential inclusion under state constraints are also provided. 2010 Mathematics Subject Classification: 49K15, 49K21, 34A60, 34K35.