Slopes and Moreau-Rockafellar Theorem

Properties of local and global slope of a function and its approximate critical points sets are studied in relation to determination of the function

Simultaneous perturbed minimization of a convergent sequence of functions

We establish a general method for simultaneously perturbing a convergent sequence of functions in such a way that the sequence of strong minima of the perturbed functions tend to the strong minimum of their limit

Abstract Subdifferential Calculus and Semi-Convex Functions

∗ The work is partially supported by NSFR Grant No MM 409/94.We develop an abstract subdifferential calculus for lower semicontinuous functions and investigate functions similar to convex functions. As application we give sufficient conditions for the integrability of a lower semicontinuous function

On Clarke-Ledyaev inequality

[Ivanov Milen; Иванов Милен]; [Zlateva Nadia; Златева Надя]We prove that Clarke-Ledyaev multidirectional mean value inequality holds for lower semicontinuous function on smooth Banach space. As application we establish a formula for the Clarke-Rockafellar directional derivative of lower semicontinuous function

Second-order subdifferentials of C^1,1 functions and optimality conditions

[Georgiev Pando Gr.; Георгиев Пандо Гр.]; [Zlateva Nadia P.; Златева Надя П.]We present second-order subdifferentials of Clarke’s type of C^1,1 functions, defined in separable Banach spaces with separable duals, i.e. of functions whose gradient mapping is locally Lipschitz. One of them is an extension of the generalized Hessian matrix of such functions in R^n, considered by J.B. H.-Urruty, J.J. Strodiot and V.H. Nguyen. Various properties of these subdifferentials are proved. Second order optimality conditions (necessary, sufficient) for constrained minimization problems with C^1,1 data are obtained