Second-order conditions in stability analysis for state constrained optimal control

摘要

The paper presents an outline of the stability results, for state-constrained optimal control problems, recently obtained in Malanowski (Appl. Math. Optim. 55, 255-271, 2007), Malanowski (Optimization, to be published), Malanowski (SIAM J. Optim., to be published). The pricipal novelty of the results is a weakening of the second-order sufficient optimality conditions, under which the solutions and the Lagrange multipliers are locally Lipschitz continuous functions of the parameter. The conditions are weakened by taking into account strongly active state constraints.