The existence of monotone solutions for a second-order functional differential inclusion is obtained in the case when the multifunction that define the inclusion is upper semicontinuous compact valued and contained in the Fréchet subdifferential of a φ-convex function of order two.

In this paper we study a nonlinear evolution inclusion of subdifferential type in Hilbert spaces. The perturbation term is Hausdorff continuous in the state variable and has closed but not necessarily convex values. Our result is a stochastic generalization of an existence theorem proved by Kravvaritis and Papageorgiou in [6].

We study subdifferential conditions of the calmness property for multifunctions representing convex constraint systems in a Banach space. Extending earlier work in finite dimensions [R. Henrion and J. Outrata, J. Math. Anal. Appl., 258 (2001), pp. 110–130], we show that, in contrast to the stronger Aubin property of a multifunction (or metric regularity of its inverse), calmness can be ensured ...

‎This paper proposes a new form of optimization problem which is a two-level programming problem with infinitely many lower level constraints‎. ‎Firstly‎, ‎we consider some lower level constraint qualifications (CQs) for this problem‎. ‎Then‎, ‎under these CQs‎, ‎we derive formula for estimating the subdifferential of its valued function‎. ‎Finally‎, ‎we present some necessary optimality condit...

A Lagrange multiplierrules that uses small generalized gradients is introduced. It includes both inequality and set constraints. The generalized gradient is the linear generalized gradient. It is smaller than the generalized gradients of Clarke and Mordukhovich but retains much of their nice calculus. Its convex hull is the generalized gradient of Michel and Penot if a function is Lipschitz. Th...

It is shown that various first and second order derivatives of the Fitzpatrick and Penot representative functions for a maximal monotone operator T , in a reflexive Banach space, can be used to represent differential information associated with the tangent and normal cones to the GraphT . In particular we obtain formula for the Proto-derivative, as well as its polar, the normal cone to the grap...