Mathematical and computational modeling of dry-cured hams in a domain of interest

El propósito de este trabajo es desarrollar un modelo computacional tridimensional, basado en el jamón numérico planteado por Harkouss, simplificándolo primero a un modelo en una dimensión para analizar matemáticamente la sensibilidad de la temperatura, concentración de sal y de agua con respecto a pequeñas variaciones de los parámetros que intervienen durante el proceso de curado de jamón. Luego avanzar a un dominio cúbico de interés, que permita describir los fenómenos físicos (transferencia de calor y masa) y biológicos (proteólisis) ocurridos durante el proceso de fabricación. De esta manera se espera dar respuesta a las necesidades del sector productivo al ofrecer nuevos enfoques tecnológicos que permita reducir el contenido de sal en sus productos y cumplir con las reglamentaciones del Ministerio de Salud de la Nación y la Cámara Argentina de la Industria de Chacinados y Afines (CAICHA).The purpose of this work is to develop a three-dimensional computational model, based on the Numerical Ham proposed by Harkouss, simplifying it first to a model in one dimension to analyze the stability of the temperature, salt and water concentration for small perturbations of the parameters that arbitrate during the ham curing process. Then to advance to a cubic domain of interest to descibe the physical phenomena (heat and mass transfer) and biological (proteolysis) of the dry-cured ham process. In this way we expected to respond to the productive sector needs by offering new technological approaches to reduce the salt content in their products and to satisfies the regulations of the Ministry of Health and the Argentine Chamber of Chacina Industry and Related (CAICHA)

Stability of the Duality Gap in Linear Optimization

In this paper we consider the duality gap function g that measures the difference between the optimal values of the primal problem and of the dual problem in linear programming and in linear semi-infinite programming. We analyze its behavior when the data defining these problems may be perturbed, considering seven different scenarios. In particular we find some stability results by proving that, under mild conditions, either the duality gap of the perturbed problems is zero or + ∞ around the given data, or g has an infinite jump at it. We also give conditions guaranteeing that those data providing a finite duality gap are limits of sequences of data providing zero duality gap for sufficiently small perturbations, which is a generic result.This research was partially supported by MINECO of Spain and FEDER of EU, Grant MTM2014-59179-C2-01 and SECTyP-UNCuyo Res. 4540/13-R

Selected Applications of Linear Semi-Infinite Systems Theory

In this paper we, firstly, review the main known results on systems of an arbitrary (possibly infinite) number of weak linear inequalities posed in the Euclidean space Rn (i.e., with n unknowns), and, secondly, show the potential power of this theoretical tool by developing in detail two significant applications, one to computational geometry: the Voronoi cells, and the other to mathematical analysis: approximate subdifferentials, recovering known results in both fields and proving new ones. In particular, this paper completes the existing theory of farthest Voronoi cells of infinite sets of sites by appealing to well-known results on linear semi-infinite systems.This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); by CONICET, Argentina, Res D No 4198/17; and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3922/19-R, Cod.06/D227, Argentina

Propiedades Lipschitzianas para el Par Dual en Optimización Lineal Cónica

Este trabajo analiza la estabilidad de los conjuntos factibles de un problema de optimización lineal cónica en dimensión infinita y de su dual asociado. A través del concepto de coderivada se establece una caracterización de la propiedad de tipo Lipschitz de las aplicaciones conjunto factible de ambos problemas. Se obtiene una fórmula para el cálculo de la constante Lipschitz de la aplicación factible del pro- blema primal en cierto punto, que coincide con la norma de la coderivada en dicho punto. El caso del dual es más complejo y se obtienen estimaciones de esta cota. Por otro lado se utiliza la noción de derivada gráfica para estimar la cota lipschitziana del problema dual en dimensión finita. Se comparan los resultados obtenidos al calcular la constante Lipschitz utilizando la coderivada y la derivada gráfica.Fil: Ridolfi, Andrea Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Luis; Argentin

Linear conic and two-stage stochastic optimization revisited via semi-infinite optimization

In this paper, we update the theory of deterministic linear semi-infinite programming, mainly with the dual characterizations of the constraint qualifications, which play a crucial role in optimality and duality. From this theory, we obtain new results on conic and two-stage stochastic linear optimization. Specifically, for conic linear optimization problems, we characterize the existence of feasible solutions and some geometric properties of the feasible set, and we also provide theorems on optimality and duality. Analogously, regarding stochastic optimization problems, we study the semi-infinite reformulation of a problem-based scenario reduction problem in two-stage stochastic linear programming, providing a sufficient condition for the existence of feasible solutions as well as optimality and duality theorems to its non-combinatorial part.This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3032/2022-R, Cod. 06/L014-T1, Argentina

On coderivatives and Lipschitzian properties of the dual pair in optimization

In this paper, we apply the concept of coderivative and other tools from the generalized differentiation theory for set-valued mappings to study the stability of the feasible sets of both the primal and the dual problem in infinite-dimensional linear optimization with infinitely many explicit constraints and an additional conic constraint. After providing some specific duality results for our dual pair, we study the Lipschitz-like property of both mappings and also give bounds for the associated Lipschitz moduli. The situation for the dual shows much more involved than the case of the primal problem.The research of this author has been partially supported by MICINN Grant MTM2008-06695-C03-01 from Spain, and by ARC Project DP110102011 from Australia

A note on primal-dual stability in infinite linear programming

In this note we analyze the simultaneous preservation of the consistency (and of the inconsistency) of linear programming problems posed in infinite dimensional Banach spaces, and their corresponding dual problems, under sufficiently small perturbations of the data. We consider seven different scenarios associated with the different possibilities of perturbations of the data (the objective functional, the constraint functionals, and the right hand-side function), i.e., which of them are known, and remain fixed, and which ones can be perturbed because of their uncertainty. The obtained results allow us to give sufficient and necessary conditions for the coincidence of the optimal values of both problems and for the stability of the duality gap under the same type of perturbations. There appear substantial differences with the finite dimensional case due to the distinct topological properties of cones in finite and infinite dimensional Banach spaces.This research was partially supported by PGC2018-097960-B-C22 of the Ministerio de Ciencia, Innovación y Universidades (MCIU), the Agencia Estatal de Investigación (AEI), and the European Regional Development Fund (ERDF); by the Australian Research Council, Project DP180100602; by CONICET, Argentina, Res D N◦ 4198/17; and by Universidad Nacional de Cuyo, Secretaría de Investigación, Internacionales y Posgrado (SIIP), Res. 3922/19-R, Cod.06/D227, Argentina