Generalized convexity: Their applications to variational problems

The aim of this paper is to show one of the generalized convexity applications, generalized monotonicity particularly, to the variational problems study. These problems are related to the search of equilibrium conditions in physical and economic environments. If convexity plays an important role in mathematical programming problems, monotonicity will play a similar role in variational problems. This paper shows some recent results about this topic

Generalized convexity: Their applications to multiobjective programming

The aim of this paper is to show some applicable results to multiobjective optimization problems and the role that the Generalized Convexity plays in them. The study of convexity for sets and functions has special relevance in the search of optimal functions, and in the development of algorithms for solving optimization problems. However, the absence of convexity implies a total loss of effectiveness of the Optimization Theory methods, ie, the results are being verified under less stringent conditions, it was what became known as Generalized convexity. The literature generated around this topic has demonstrated its importance both from a theoretical point of view as practical, but it has also generated an enormous amount of papers with little scientific input

Optimality and duality on Riemannian manifolds

Our goal in this paper is to translate results on function classes that are characterized by the property that all the Karush-Kuhn-Tucker points are efficient solutions, obtained in Euclidean spaces to Riemannian manifolds. We give two new characterizations, one for the scalar case and another for the vectorial case, unknown in this subject literature. We also obtain duality results and give examples to illustrate it.Ministerio de Economía y Competitivida

New optimality conditions for multiobjective fuzzy programming problems

In this paper we study fuzzy multiobjective optimization problems de ned for n variables. Based on a new p-dimensional fuzzy stationary-point de nition, necessary e ciency conditions are obtained. And we prove that these conditions are also su cient under new fuzzy generalized convexity notions. Furthermore, the results are obtained under general di erentiability hypothesis.The research in this paper has been supported by Fondecyt-Chile, project 1151154 and by Ministerio de Economía y Competitividad, Spain, through grant MINECO/FEDER(UE) MTM2015-66185-P

A Better Approach for Solving a Fuzzy Multiobjective Programming Problem by Level Sets

In this paper, we deal with the resolution of a fuzzy multiobjective programming problem using the level sets optimization. We compare it to other optimization strategies studied until now and we propose an algorithm to identify possible Pareto efficient optimal solutions

Different optimum notions for fuzzy functions and optimality conditions associated

Fuzzy numbers have been applied on decision and optimization problems in uncertain or imprecise environments. In these problems, the necessity to define optimal notions for decision-maker’s preferences as well as to prove necessary and sufficient optimality conditions for these optima are essential steps in the resolution process of the problem. The theoretical developments are illustrated and motivated with several numerical examples.The research in this paper has been supported by MTM2015-66185 (MINECO/FEDER, UE) and Fondecyt-Chile, Project 1151154

Approximate Efficient Solutions of the Vector Optimization Problem on Hadamard Manifolds via Vector Variational Inequalities

This article has two objectives. Firstly, we use the vector variational-like inequalities problems to achieve local approximate (weakly) efficient solutions of the vector optimization problem within the novel field of the Hadamard manifolds. Previously, we introduced the concepts of generalized approximate geodesic convex functions and illustrated them with examples. We see the minimum requirements under which critical points, solutions of Stampacchia, and Minty weak variational-like inequalities and local approximate weakly efficient solutions can be identified, extending previous results from the literature for linear Euclidean spaces. Secondly, we show an economical application, again using solutions of the variational problems to identify Stackelberg equilibrium points on Hadamard manifolds and under geodesic convexity assumptions

Necessary and sufficient conditions for interval-valued differentiability

This paper presents necessary and sufficient conditions for generalized Hukuhara differentiability of interval-valued functions and counterexamples of some equivalences previously presented in the literature, for which important results are based on. Moreover, applications of interval generalized Hukuhara differentiability are presented

Comparative study between nail retraining with gauze bandaging and the nail remodeling with acrylics as a conservative treatment for stage I and IIa onychocryptosis

Objective: Onychocryptosis is one of the most prevalent onychopathies, being a frequent reason for consultation in podiatric clinical practice. Conservative treatments are the first therapeutic choice, with nail remodeling using clotrimazole gel emerging as an alternative, although its medium-term effectiveness is unknown. The objective of this study was therefore to compare the efficacy of the technique of nail retraining using gauze bandaging with that of nail remodeling for the conservative treatment of stage I and IIA onychocryptosis. Methods: An analytical, randomized clinical trial study was performed following a longitudinal and prospective design. A sample was selected of 20 subjects presenting stage I and IIA onychocryptosis. Of these, 10 cases formed the group of nail retraining using gauze bandaging, and the other 10 the nail remodeling group. The presence of recurrence in a 3-month period was evaluated. Results: Before the intervention, the patients in the retraining group presented pain of 6.7 ± 1.9 vs. 6.8 ± 1.6 in the remodeling group, with no significant difference between the two (p = 0.900). After the 3-month follow-up period, seven of the retraining group patients presented recurrence of onychocryptosis vs. only one in the remodeling group. Conclusion: The technique of nail remodeling has a lower recurrence rate than that of nail retraining with gauze bandaging, with the pain, inflammation, and infection reported being less, and with greater patient satisfactio

Crisis of the social and emergence of sociality in the new scenarios of identity: The San Francisco district of Bilbao

El barrio de San Francisco, en Bilbao, está pasando por un profundo proceso de transformación urbana en el que están convergiendo diferentes dinámicas económicas (especulación inmobiliaria), sociales (emergencia de asociaciones y movimientos sociales) y políticas (planes de rehabilitación) . Con el fin de explicar estas transformaciones, trabajaremos en este artículo con dos hipótesis: la de la gentrificación y la de la crisis de las instituciones sociales (política, religión y trabajo) que articulaban tradicionalmente la sociedad. Para compensar las limitaciones de ambas hipótesis las redefiniremos como meras condiciones de posibilidad de la emergencia de nuevas formas de socialidad, de despolitización de los significados y de la producción de nuevos espacios. De este modo, San Francisco constituye un cronotopo interesante en la medida en que provoca cierta difuminación en las configuraciones sociológicas y sociales