Calmness of the Feasible Set Mapping for Linear Inequality Systems

In this paper we deal with parameterized linear inequality systems in the n-dimensional Euclidean space, whose coefficients depend continuosly on an index ranging in a compact Hausdorff space. The paper is developed in two different parametric settings: the one of only right-hand-side perturbations of the linear system, and that in which both sides of the system can be perturbed. Appealing to the backgrounds on the calmness property, and exploiting the specifics of the current linear structure, we derive different characterizations of the calmness of the feasible set mapping, and provide an operative expresion for the calmness modulus when confined to finite systems. In the paper, the role played by the Abadie constraint qualification in relation to calmness is clarified, and illustrated by different examples. We point out that this approach has the virtue of tackling the calmness property exclusively in terms of the system’s data.

Inequality in analgesic prescription in Spain: a gender development issue

Objectives: It is well known that sex differences in analgesic prescription are not merely the logical result of greater prevalence of pain in women, since this therapeutic variability is related to factors such as educational level or social class. This study aims to analyse the relationship between analgesic prescription and gender development in different regions of Spain. Methods: Cross-sectional study of sex-differences in analgesic prescription according to the gender development of the regions studied. Analgesic prescription, pain and demographic variables were obtained from the Spanish Health Interview Survey in 2006. Gender development was measured with the Gender Development Index (GDI). A logistic regression analysis was conducted to compare analgesic prescription by sex in regions with a GDI above or below the Spanish average. Results: Once adjusted by pain, age and social class, women were more likely to be prescribed analgesics than men, odds ratio (OR) = 1.74 (1.59-1.91), as residents in regions with a lower GDI compared with those in region with a higher GDI: ORWomen = 1.26 (1.12-1.42), ORMen = 1.30 (1.13-1.50). Women experiencing pain in regions with a lower GDI were more likely than men to be treated by a general practitioner rather than by a specialist, OR = 1.32 (1.04-1.67), irrespective of age and social class. Conclusions: Gender bias may be one of the pathways by which inequalities in analgesic treatment adversely affect women's health. Moreover, research into the adequacy of analgesic treatment and the possible medicalisation of women should consider contextual factors, such as gender development.

Water speech: energy, power and inequality in Brazil

The documentary is available in Portuguese at the following link: http://hdl.handle.net/10045/17580

Quantitative stability of linear infinite inequality systems under block perturbations with applications to convex systems

The original motivation for this paper was to provide an efficient quantitative analysis of convex infinite (or semi-infinite) inequality systems whose decision variables run over general infinite-dimensional (resp. finite-dimensional) Banach spaces and that are indexed by an arbitrary fixed set J. Parameter perturbations on the right-hand side of the inequalities are required to be merely bounded, and thus the natural parameter space is l ∞(J). Our basic strategy consists of linearizing the parameterized convex system via splitting convex inequalities into linear ones by using the Fenchel–Legendre conjugate. This approach yields that arbitrary bounded right-hand side perturbations of the convex system turn on constant-by-blocks perturbations in the linearized system. Based on advanced variational analysis, we derive a precise formula for computing the exact Lipschitzian bound of the feasible solution map of block-perturbed linear systems, which involves only the system’s data, and then show that this exact bound agrees with the coderivative norm of the aforementioned mapping. In this way we extend to the convex setting the results of Cánovas et al. (SIAM J. Optim. 20, 1504–1526, 2009) developed for arbitrary perturbations with no block structure in the linear framework under the boundedness assumption on the system’s coefficients. The latter boundedness assumption is removed in this paper when the decision space is reflexive. The last section provides the aimed application to the convex case.

Voronoi cells via linear inequality systems

The theory and methods of linear algebra are a useful alternative to those of convex geometry in the framework of Voronoi cells and diagrams, which constitute basic tools of computational geometry. As shown by Voigt and Weis in 2010, the Voronoi cells of a given set of sites T, which provide a tesselation of the space called Voronoi diagram when T is finite, are solution sets of linear inequality systems indexed by T. This paper exploits systematically this fact in order to obtain geometrical information on Voronoi cells from sets associated with T (convex and conical hulls, tangent cones and the characteristic cones of their linear representations). The particular cases of T being a curve, a closed convex set and a discrete set are analyzed in detail. We also include conclusions on Voronoi diagrams of arbitrary sets.

The evolution of gender inequality in tourism employment in Spain

Evolución de la desigualdad por género del empleo turístico en España. Si bien la inversión en capital laboral femenino en la industria turística ha aumentado en los últimos años y parece que la discriminación en el acceso a puestos directivos ha descendido, se siguen produciendo diferentes situaciones de desigualdad. La mujer mantiene un salario por debajo del hombre y han aparecido nuevas formas de segregación ocupacional entre hombres y mujeres e incluso entre las propias mujeres: la división entre trabajo a tiempo parcial y completo es un buen ejemplo de este proceso. La hipótesis que se plantea este trabajo es que esa combinación entre tiempo de trabajo remunerado (ámbito público) y no remunerado (ámbito privado, doméstico) es un obstáculo que provoca el acceso de los varones a empleos hasta ahora "femeninos"; así mismo, se observará la calidad del empleo turístico desde la perspectiva de género.

From the Farkas Lemma to the Hahn–Banach Theorem

This paper provides new versions of the Farkas lemma characterizing those inequalities of the form f(x) ≥ 0 which are consequences of a composite convex inequality (S ◦ g)(x) ≤ 0 on a closed convex subset of a given locally convex topological vector space X, where f is a proper lower semicontinuous convex function defined on X, S is an extended sublinear function, and g is a vector-valued S-convex function. In parallel, associated versions of a stable Farkas lemma, considering arbitrary linear perturbations of f, are also given. These new versions of the Farkas lemma, and their corresponding stable forms, are established under the weakest constraint qualification conditions (the so-called closedness conditions), and they are actually equivalent to each other, as well as equivalent to an extended version of the so-called Hahn–Banach–Lagrange theorem, and its stable version, correspondingly. It is shown that any of them implies analytic and algebraic versions of the Hahn–Banach theorem and the Mazur–Orlicz theorem for extended sublinear functions.

Constraint qualifications in linear vector semi-infinite optimization

Linear vector semi-infinite optimization deals with the simultaneous minimization of finitely many linear scalar functions subject to infinitely many linear constraints. This paper provides characterizations of the weakly efficient, efficient, properly efficient and strongly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The global constraint qualifications are illustrated on a collection of selected applications.

Robust Solutions of MultiObjective Linear Semi-Infinite Programs under Constraint Data Uncertainty

The multiobjective optimization model studied in this paper deals with simultaneous minimization of finitely many linear functions subject to an arbitrary number of uncertain linear constraints. We first provide a radius of robust feasibility guaranteeing the feasibility of the robust counterpart under affine data parametrization. We then establish dual characterizations of robust solutions of our model that are immunized against data uncertainty by way of characterizing corresponding solutions of robust counterpart of the model. Consequently, we present robust duality theorems relating the value of the robust model with the corresponding value of its dual problem.

Three-dimensional planar model estimation using multi-constraint knowledge based on k-means and RANSAC

Plane model extraction from three-dimensional point clouds is a necessary step in many different applications such as planar object reconstruction, indoor mapping and indoor localization. Different RANdom SAmple Consensus (RANSAC)-based methods have been proposed for this purpose in recent years. In this study, we propose a novel method-based on RANSAC called Multiplane Model Estimation, which can estimate multiple plane models simultaneously from a noisy point cloud using the knowledge extracted from a scene (or an object) in order to reconstruct it accurately. This method comprises two steps: first, it clusters the data into planar faces that preserve some constraints defined by knowledge related to the object (e.g., the angles between faces); and second, the models of the planes are estimated based on these data using a novel multi-constraint RANSAC. We performed experiments in the clustering and RANSAC stages, which showed that the proposed method performed better than state-of-the-art methods.

Health inequality between immigrants and natives in Spain: the loss of the healthy immigrant effect in times of economic crisis

Background: The immigrant population living in Spain grew exponentially in the early 2000s but has been particularly affected by the economic crisis. This study aims to analyse health inequalities between immigrants born in middle- or low-income countries and natives in Spain, in 2006 and 2012, taking into account gender, year of arrival and socioeconomic exposures. Methods: Study of trends using two cross-sections, the 2006 and 2012 editions of the Spanish National Health Survey, including residents in Spain aged 15–64 years (20 810 natives and 2950 immigrants in 2006, 14 291 natives and 2448 immigrants in 2012). Fair/poor self-rated health, poor mental health (GHQ-12 > 2), chronic activity limitation and use of psychotropic drugs were compared between natives and immigrants who arrived in Spain before 2006, adjusting robust Poisson regression models for age and socioeconomic variables to obtain prevalence ratios (PR) and 95% confidence interval (CI). Results: Inequalities in poor self-rated health between immigrants and natives tend to increase among women (age-adjusted PR2006 = 1.39; 95% CI: 1.24–1.56, PR2012 = 1.56; 95% CI: 1.33–1.82). Among men, there is a new onset of inequalities in poor mental health (PR2006 = 1.10; 95% CI: 0.86–1.40, PR2012 = 1.34; 95% CI: 1.06–1.69) and an equalization of the previously lower use of psychotropic drugs (PR2006 = 0.22; 95% CI: 0.11–0.43, PR2012 = 1.20; 95% CI: 0.73–2.01). Conclusions: Between 2006 and 2012, immigrants who arrived in Spain before 2006 appeared to worsen their health status when compared with natives. The loss of the healthy immigrant effect in the context of a worse impact of the economic crisis on immigrants appears as potential explanation. Employment, social protection and re-universalization of healthcare would prevent further deterioration of immigrants’ health status.

Intimate partner violence among women in Spain: the impact of regional-level male unemployment and income inequality

Background: Intimate partner violence (IPV) against women is a complex worldwide public health problem. There is scarce research on the independent effect on IPV exerted by structural factors such as labour and economic policies, economic inequalities and gender inequality. Objective: To analyse the association, in Spain, between contextual variables of regional unemployment and income inequality and individual women’s likelihood of IPV, independently of the women’s characteristics. Method: We conducted multilevel logistic regression to analyse cross-sectional data from the 2011 Spanish Macrosurvey of Gender-based Violence which included 7898 adult women. The first level of analyses was the individual women’ characteristics and the second level was the region of residence. Results: Of the survey participants, 12.2% reported lifetime IPV. The region of residence accounted for 3.5% of the total variability in IPV prevalence. We determined a direct association between regional male long-term unemployment and IPV likelihood (P = 0.007) and between the Gini Index for the regional income inequality and IPV likelihood (P < 0.001). Women residing in a region with higher gender-based income discrimination are at a lower likelihood of IPV than those residing in a region with low gender-based income discrimination (odds ratio = 0.64, 95% confidence intervals: 0.55–0.75). Conclusions: Growing regional unemployment rates and income inequalities increase women’s likelihood of IPV. In times of economic downturn, like the current one in Spain, this association may translate into an increase in women’s vulnerability to IPV.

Constraint qualifications in convex vector semi-infinite optimization

Convex vector (or multi-objective) semi-infinite optimization deals with the simultaneous minimization of finitely many convex scalar functions subject to infinitely many convex constraints. This paper provides characterizations of the weakly efficient, efficient and properly efficient points in terms of cones involving the data and Karush–Kuhn–Tucker conditions. The latter characterizations rely on different local and global constraint qualifications. The results in this paper generalize those obtained by the same authors on linear vector semi-infinite optimization problems.