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.

Calmness modulus of linear semi-infinite programs

Our main goal is to compute or estimate the calmness modulus of the argmin mapping of linear semi-infinite optimization problems under canonical perturbations, i.e., perturbations of the objective function together with continuous perturbations of the right-hand side of the constraint system (with respect to an index ranging in a compact Hausdorff space). Specifically, we provide a lower bound on the calmness modulus for semi-infinite programs with unique optimal solution which turns out to be the exact modulus when the problem is finitely constrained. The relationship between the calmness of the argmin mapping and the same property for the (sub)level set mapping (with respect to the objective function), for semi-infinite programs and without requiring the uniqueness of the nominal solution, is explored, too, providing an upper bound on the calmness modulus of the argmin mapping. When confined to finitely constrained problems, we also provide a computable upper bound as it only relies on the nominal data and parameters, not involving elements in a neighborhood. Illustrative examples are provided.

Factores que influyen en la decisión de utilizar anestesia epidural en las mujeres

Justificación: La inmigración en España es un fenómeno de gran importancia que repercute en el área de la salud. Objetivo: Investigar la relación entre la elección de la anestesia epidural y la nacionalidad de la mujer, y a su vez, observar si influyen además otros factores en esta decisión. Diseño y Metodología: Estudio cuantitativo, transversal y descriptivo con una muestra de 634 mujeres que han dado a luz en el Hospital del Noroeste de la Región de Murcia. Las variables seleccionadas fueron: antecedentes obstétricos, edad, tipo de anestesia, nacionalidad de la mujer y motivo por el rechazo de la anestesia epidural. Resultados: El 8,51% de las mujeres que dieron a luz en el hospital del Noroeste de la Región de Murcia durante el año 2010 fueron inmigrantes. En cuanto a la nacionalidad, el 20,37% de las mujeres inmigrantes no han utilizado ningún tipo de anestesia. Se ha encontrado una significante diferencia con las mujeres no inmigrantes españolas en las que sólo el 4,31% la rechazó (P<0,001). En relación a los abortos, las mujeres que no prefieren ningún tipo de anestesia son aquellas que sí han tenido abortos (P<0.05). Las edades más jóvenes de las mujeres, de 16 a 25 años, se relaciona con el no uso de la anestesia epidural (P<0,05). Conclusión: Las mujeres inmigrantes hacen menos uso de la anestesia epidural. Es un reto para la enfermera aprender las diferentes culturas ya que realiza su trabajo en una sociedad cada vez más multicultural.

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.