A a set-valued optimization problem min<Subscript> C </Subscript> F(x), x ∈X <Subscript>0</Subscript>, is considered, where X <Subscript>0</Subscript> ⊂ X, X and Y are normed spaces, F: X <Subscript>0</Subscript> ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x <Superscript>0</Superscript>,y <Superscript>0</Superscript>), y <Superscript>0</Superscript> ∈F(x <Superscript>0</Superscript>), and are called...</superscript></superscript></superscript></superscript></subscript></subscript></subscript></subscript>

A a set-valued optimization problem min C F(x), x ∈X 0 , is considered, where X 0 ⊂ X, X and Y are normed spaces, F: X 0 ⊂ Y is a set-valued function and C ⊂ Y is a closed cone. The solutions of the set-valued problem are defined as pairs (x 0 ,y 0 ), y 0 ∈F(x 0 ), and are called...

In this paper, we extend the concept of cone-convexlikeness of single-valued maps to set-valued maps and study super efficiency in cone-convexlike vector optimization with set-valued maps. Under the assumption of the cone-convexlikeness, some characterizations of super efficiency are established...

In this paper, we extend the concept of cone-convexlikeness of single-valued maps to set-valued maps and study super efficiency in cone-convexlike vector optimization with set-valued maps. Under the assumption of the cone-convexlikeness, some characterizations of super efficiency are established...

The main aim of this paper is to generalize the notion of pseudolinearity to nondifferentiable functions and to obtain characterizations for such functions. Under the assumption of pseudolinearity, a characterization for the solution sets of an optimization problem and a variational inequality...

In this work we provide a characterization of C 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 1,1 functions is equivalent to the class of functions with...

Many definitions of second order generalized derivatives have been introduced to obtain optimality conditions for optimization problems involving C(1,1) data. The aim of this paper is to show some relations among these definitions and to study necessary and sufficient optimality conditions for...

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 work we provide a characterization of C1,1 functions on Rn (that is,diferentiable with locally Lipschitz partial derivatives) by means of second directional divided differences. In particular, we prove that the class of C1,1 functions is equivalent to the class of functions with bounded...