In this paper, we follow Kuroiwa’s set approach in set optimization, which proposes to compare values of a set-valued objective map F respect to various set order relations. We introduce a Hausdorff-type distance relative to an ordering cone between two sets in a Banach space and use it to define a directional derivative for F . We show that the distance has nice properties regarding set order ...

The optimization of multimodal functions is a challenging task, in particular when derivatives are not available for use. Recently, in a directional direct search framework, a clever multistart strategy was proposed for global derivative-free optimization of single objective functions. The goal of the current work is to generalize this approach to the computation of global Pareto fronts for mul...

Many image-rotation invariant texture classification approaches have been presented. However, image rotation is not necessarily the same as surface rotation. This paper proposes a novel scheme that is surface-rotation invariant. It uses magnitude spectra of the partial derivatives of the surface obtained using photometric stereo. Unfortunately the partial derivative operator is directional. It ...

This work is intended to give some ideas to extract motion information from an image sequence. A directional energy is defined in terms of the 1-D Hermite transform coefficients of local projections. Each projection is described by the Hermite transform resulting in a directional derivative analysis of the input at a given scale. Gaussian-derivative operators have long been used in computer vis...

In this paper, we consider a class of nonsmooth, nonconvex constrained optimization problems where the objective function may be not Lipschitz continuous and the feasible set is a general closed convex set. Using the theory of the generalized directional derivative and the Clarke tangent cone, we derive a first order necessary optimality condition for local minimizers of the problem, and define...

This paper is devoted to the study of gH-Clarke derivative for interval-valued functions. To find properties derivative, concepts limit superior, inferior, and sublinear functions are studied in sequel. It proved that upper a gH-Lipschitz continuous function (IVF) always exists. For convex IVF, found be identical with gH-directional derivative. observed IVF. Several numerical examples provided ...

Matrix valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, B-derivative, directional derivative, and se...

The paper is devoted to the investigation of directional derivatives and the cone of decrease directions for convex operators on Banach spaces. We prove a condition for the existence of directional derivatives which does not assume regularity of the ordering cone K. This result is then used to prove that for continuous convex operators the cone of decrease directions can be represented in terms...

Matrix-valued functions play an important role in the development of algorithms for semidefinite programming problems. This paper studies generalized differential properties of such functions related to nonsmooth-smoothing Newton methods. The first part of this paper discusses basic properties such as the generalized derivative, Rademacher’s theorem, -derivative, directional derivative, and sem...

Many multi-dimensional signal processing problems require the computation of signal gradients or directional derivatives. Traditional derivative estimates based on adjacent or central diierences are often inappropriate for multi-dimensional problems. As replacements for these traditional operators, we design a set of matched pairs of derivative lters and lowpass pre-lters. We demonstrate the su...