Stability and sensitivity of solutions to optimal control problems for systems with control appearing linearly (Q1095390)

Optimal control problems for nonlinear ordinary differential equations are considered, with data depending on parameters. The control variables enter affinely in the dynamics. The cost functional and the control constraints are convex. Under suitable constraint regularity assumptions it is shown that the optimal solutions as well as the corresponding Lagrange multipliers are locally Lipschitz continuous functions of the parameters. Directional differentiability is also obtained.