Differential stability of solutions to constrained optimization problems

In this paper the differential stability of solutions to constrained optimization problems is investigated. The form of right-derivatives of optimal solutions to such problems, with respect to a real parameter, is derived. The right-derivative of the optimal control with respect to parameter for an optimal control problem for parabolic equation is obtained in the form of the optimal solution to an auxiliary optimal control problem. A method for determination of the second right-derivative of the optimal solutions to constrained optimization problems is proposed. Several examples are provided.This research has been supported by INRIA, in the framework of a collaboration between the project Théorie des Systèmes and the Systems Research Institute of the Polish Academy of Sciences.