In this paper we survey some notions of generalized derivative for C 1,1 functions. Furthermore some optimality conditions and numerical methods for nonlinear minimization problems involving C1,1 data are studied.

In this note a mean value theorem for continuous vector functions is introduced by mollified derivatives and smooth approximations

The class of strongly semicontinuous functions is considered. For these functions the notion of mollified derivatives, introduced by Ermoliev, Norkin and Wets, is extended to the second order. By means of a generalized Taylor's formula, second order necessary and sufficient conditions are proved...

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 work we provide a characterization of Ck,1 functions on Rn (that ik K times differentiable with locally Lipschitz k-th derivatives) by means of (k+1)-th divided differences and Riemann derivatives. In particular we prove that the class of Ck,1 functions is equivalent to the class of...

In this paper we deal with a Fritz John type constrained vector optimization problem. In spite that there are many concepts of solutions for an unconstrained vector optimization problem, we show the possibility “to double” the number of concepts when a constrained problem is considered. In...

In this paper we introduce a generalized second-order Riemann-type derivative for C 1,1 vector functions and use it to establish necessary and sufficient optimality conditions for vector optimization problems. We show that these conditions are stronger than those obtained by means of the...

In this paper we consider the vector optimization problem minC f(x), g(x) 2 -K, where f : Rn ! Rm and g : Rn Rp are C0,1 functions and C Rm and K Rp are closed convex cones. We give several notions of solutions (efficiency concepts), among them the notion of a properly efficient point...

In this paper, we give a survey on well-posedness notions of Tykhonov's type for vector optimization problems and the links between them with respect to the classification proposed by Miglierina, Molho and Rocca. We consider also the notions of extended well-posedness introduced by X.X. Huang in...

In this paper we introduce notions of well-posedness for a vector optimization problem and for a vector variational inequality of differential type, we study their basic properties and we establish the links among them. The proposed concept of well-posedness for a vector optimization problem...