In this article we examine to necessary and sufficient optimality conditions for interval optimization problems. We introduce a new concept of stationary point for an interval-valued function based on the gH-derivative. We show the importance the this concept from a practical and computational point of view. We introduce a new concept of invexity for gH-differentiable interval-valued function w...

Nonsmooth operator equations in function spaces are considered, which depend on perturbation parameters. The nonsmoothness arises from a projection onto an admissible interval. Lipschitz stability in L∞ and Bouligand differentiability in L of the parameter-to-solution map are derived. An adjoint problem is introduced for which Lipschitz stability and Bouligand differentiability in L∞ are obtain...

space. For ( ) 1 h L X ∈ ,Γ,μ and Z∈Γ with indicator function ( ) Z I L X ∞ ∈ ,Γ, , μ the integral Z h ∫ dμ will be denoted by Z h I , . Now, we shall define the notion of differentiability for n-set functions. Morris [7] introduced differentiability for set functions and Corley [4] defined this notion for n -set functions. A function : Γ→ φ ! is said to be differentiable at T if there exists (...

We consider flows of ordinary differential equations (ODEs) driven by path differentiable vector fields. Path functions constitute a proper subclass Lipschitz which admit conservative gradients, notion generalized derivative compatible with basic calculus rules. Our main result states that such inherit the differentiability property driving field. show indeed forward propagation derivatives giv...

We investigate optimality conditions for optimization problems constrained by a class of variational inequalities of the second kind. Based on a nonsmooth primal-dual reformulation of the governing inequality, the differentiability of the solution map is studied. Directional differentiability is proved both for finite-dimensional and function space problems, under suitable assumptions on the ac...