Reflexive Cones

Reflexive cones in Banach spaces are cones with weakly compact intersection with the unit ball. In this paper we study the structure of this class of cones. We investigate the relations between the notion of reflexive cones and the properties of their bases. This allows us to prove a characterization of reflexive cones in term of the absence of a subcone isomorphic to the positive cone of \ell_{1}. Moreover, the properties of some specific classes of reflexive cones are investigated. Namely, we consider the reflexive cones such that the intersection with the unit ball is norm compact, those generated by a Schauder basis and the reflexive cones regarded as ordering cones in a Banach spaces. Finally, it is worth to point out that a characterization of reflexive spaces and also of the Schur spaces by the properties of reflexive cones is given.Comment: 23 page

EXPERIENCIA EDUCATIVA : TALLER DE RECURSOS NATURALES II

El Taller de Recursos Naturales II (TRN II) se desarrolla durante el 2do cuatrimestre del segundo año de Agronomía. La información obtenida por los alumnos es utilizada en el Taller de Producción Vegetal en el 4to Año. De acuerdo a la estructura y lineamientos del Plan de Estudios, el TRN II integra actividades de las asignaturas dictadas en ese cuatrimestre como: Propiedades Edáficas y Fertilidad, Fisiología Vegetal, Genética Básica y Aplicada y Agrometeorología, además de Ecología y Zoología Agrícola, asignaturas de tercero y cuarto año respectivamente. Tiene como objetivo conducir al alumno hacia una compresión global de los factores que afectan el crecimiento de las plantas con el fin de mantener o aumentar la producción, dentro del marco de una agricultura sustentable. Finaliza con una puesta en común donde se interpretan los resultados en términos ecofisiológicos y de interacción genotipo-ambiente, utilizando información obtenida de las demás asignaturas. Así, otorga a los futuros profesionales la capacidad de analizar los conocimientos adquiridos a campo y en el laboratorio, a la luz de los factores investigados durante el desarrollo del Taller

Invex functions on differentiable manifolds

The aim of this work is to prove the sufficiency of Kuhn-Tucker conditions in the frame of invex programming on differentiable manifolds. In addition we prove that the compact manifolds do not admit nonconstant invex function

Stability in vector optimization

The aim of this work is to characterize the various sets of solutions of a vector optimization problem by means of a unique special scalarizing function. The different efficient frontiers are found as optimal scalar solutions according to a more restrictive definition of minimality: strict minima, sharp minima, well-posed minima. Moreover we link the notion of proper efficiency to some sort of stability of the scalar problem. In order to this goal, we study the convergence of the solutions of a suitable family of perturbed problems using the Kuratowski set-convergence

Box-constrained multiobjective optimization: a gradient-like method without "a priori" scalarization

The aim of this paper is the development of an algorithm to find the critical points of a box-constrained multi-objective optimization problem. The proposed algorithm is an interior point method based on suitable directions that play the role of gradient-like directions for the vector objective function. The method does not rely on an \u2018\u2018a priori\u2019\u2019 scalarization and is based on a dynamic system defined by a vector field of descent directions in the considered box. The key tool to define the mentioned vector field is the notion of vector pseudogradient. We prove that the limit points of the solutions of the system satisfy the Karush\u2013Kuhn\u2013Tucker (KKT) first order necessary condition for the box-constrained multi-objective optimization problem. These results allow us to develop an algorithm to solve box-constrained multi-objective optimization problems. Finally, we consider some test problems where we apply the proposed computational method. The numerical experience shows that the algorithm generates an approximation of the local optimal Pareto front representative of all parts of optimal front

Sectionwise connected sets in vector optimization

We introduce the notion of sectionwise connected set as a new tool to investigate nonconvex vector optimization. Indeed, the image of a K-convex set through a K-quasiconnected vector function is proved to be sectionwise connected. Some properties of the minimal frontiers of sectionwise connected sets are studied