The results from classical asymptotic theory typically require assumptions of pointwise differentiability of a criterion function with respect an unknown parameter. Taylor expansion about some " true " value in the parameter space then gives a quadratic approximation to the criterion function, within error terms that can be bounded using the remainder from the Taylor expansion. With appropriate...

In this paper we study optimization problems with infinite many inequality constraints on a Banach space where the objective function and the binding constraints are locally Lipschitz‎. ‎Necessary optimality conditions and regularity conditions are given‎. ‎Our approach are based on the Michel-Penot subdifferential.

The paper investigates the stability of the solutions of linearquadratic optimal control problems with bang-bang controls in terms of metric sub-regularity and bi-metric regularity. New sufficient conditions for these properties are obtained, which strengthen the known conditions for sub-regularity and extend the known conditions for bi-metric regularity to Bolza-type problems.

We define strong regularity of a parametric interval matrix and give conditions that characterize it. The new conditions give a better estimation for regularity of a parametric matrix than the conditions used so far. Verifiable sufficient regularity conditions are also presented for parametric matrices. The new sufficient conditions motivate a generalization of Rump’s parametric fixed-point ite...

in this paper we study optimization problems with infinite many inequality constraints on a banach space where the objective function and the binding constraints are locally lipschitz‎. ‎necessary optimality conditions and regularity conditions are given‎. ‎our approach are based on the michel-penot subdifferential.