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>

In this paper some second order necessary and sucient conditions aregiven for unconstrained and constrained optimization problems involving C1functions. A generalized derivative is obtained by approximation with smoothfunctions and it collapses to Clarke's definition when C(1,1) data are...

In this paper second-order 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 the classical...

Directional derivatives are the ideal tool to model simultaneous shifts of the instruments of economic policy. Provided the equilibrium solution of an oligolistic model are differentiable with respect to the parameter, such a problem can be easily solved considering shift in single instruments,...

A function <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$${f : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> , where Ω is a convex subset of the linear space X, is said to be d.c. (difference of convex) if f =  g − h with <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$${g, h : \Omega \to \mathbb{R}}$$</EquationSource> </InlineEquation> convex functions. While d.c. functions find various applications, especially in optimization, the...</equationsource></inlineequation></equationsource></inlineequation>

D. V. Luu and P. T. Kien propose in Soochow J. Math. 33 (2007), 17-31, higher-order conditions for strict efficiency of vector optimization problems based on the derivatives introduced by I. Ginchev in Optimization 51 (2002), 47-72. These derivatives are defined for scalar functions and in their...

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

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...

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