LIPSCHITZIAN STABILITY IN NONLINEAR CONTROL AND OPTIMIZATION

This paper studies Lipschitz properties, relative to the parameter p, of the set of solutions to problems of the form Find z is-an-element-of OMEGA(p) such that T(p)(z) is-an-element-of F(p)(z). As applications, various problems in control and optimization are examined, focusing in particular on the stability of the feasible set of a control problem, and the stability of solutions of infinite-dimensional mathematical programs and optimal control problems. In another application, an estimate is obtained for the error in the Euler approximation to an optimal control problem.