Many definitions of second-order generalized derivatives have been introduced to obtain optimality conditions for optimization problems with C wedge(1,1) data. The aim of this note is to show some relations among these definitions

In this paper some second order necessary and sufficient conditions are given for unconstrained and constrained optimization problems involving C^1 functions. A generalized derivative is obtained by approximation with smooth functions and it collapses to Clarke's definition when C^(1,1) data are...

In this paper some new contractive operators on C([a,b]) of IFS type are built. Inverse problems are introduced and studied by convex optimization problems. A stability result and some optimality conditions are given

In this paper we survey some notions of generalized derivatives for C wedge(1,1) functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C wedge(1,1) data are studied

In this work we provide a characterization of C wedge(1,1) functions on Rn (that is, differentiable with locally Lipschitz partial derivatives)by means of second directional divided differences. In particular, we prove that the class of C wedge(1,1) functions is equivalent to the class of...

Smoothing methods, extensively used for solving mathematical programming problems and applications, are applied in this paper to approximate some optimization problems arising in the theory of generalized support vector machines. A nonlinear model, which generalizes some previous works, is...

In this paper second-order necessary optimality conditions for nonsmooth vector optimization problems are given by smooth approximations. We extend to the vector case the approach introduced by Ermoliev, Norkin and Wets to define generalized derivatives for discontinuous functions as limit of...

Several methods are currently available to simulate paths of the Brownian motion. In particular, paths of the BM can be simulated using the properties of the increments of the process like in the Euler scheme, or as the limit of a random walk or via L2 decomposition like the...