06/D156
Estabilidad en Programación Semi-Infinita (continuación).
ESTABILITY IN SEMI-INFINITE PROGRAMMING (continuation).
Director: VERA, Virginia Norma
Correo Electrónico: vvera@uncu.edu.ar
Co-Director: FARES, Graciela Yasmín
Integrantes: GAYA, Verónica; GOBERNA, Miguel A.; LARRIQUETA, Mercedes; OCHOA, Pablo; RIDOLFI, Andrea; SIMONDI, Sebastián; TODOROV, Maxim; ZARAGOZA, Liliana.
Resumen Técnico: Se busca estudiar estabilidad en programación lineal semi-infinita (LSIP), en programación convexa semi-infinita (CSIP)) y en convexidad abstracta, hallando nuevos resultados con respecto a los mismos. Se plantea: 1) Determinar condiciones locales más débiles para caracterizar el conjunto factible y el conjunto optimal de problemas de programación semi-infinita lineal, cuando el conjunto de coeficientes del sistema de restricciones no es acotado. 2) Hallar condiciones necesarias y/o suficientes para la estabilidad del estado del problema primal y del problema dual en programación lineal semi-infinita, en particular se busca caracterizar la partición primal-dual (según la calidad de inconsistencia, acotación, no acotación) del espacio de parámetros para sistemas no necesariamente continuos. 3) Extender resultados sobre estabilidad obtenidos en LSIP y CSIP al contexto convexo abstracto. Se propone la formación de recursos humanos: a nivel de posgrado, a través de dos tesis de maestría y de dos tesis de doctorado; a nivel de grado con la incorporación de alumnos de licenciatura.
Summary: The aim of this project is to study stability in mathematical programming (Semi-infinite Linear Programming (LSIP), Semi-infinite Convex Programming (CSIP)) and also in abstract convexity in order to establish new results. The stability, under perturbations of all the coefficients of systems of infinitely many inequalities is analyzed from different points of view (lower semicontinuity, continuity in the Bouligand sense, Lipschitz continuity, metric regularity). We consider the following themes: 1) Different concepts of extended active constraints at a given point provide useful local information about the solution set of linear semi-infinite systems and about the optimal set in linear semi-infinite programming, always under the assumption that the set of left-hand-side vectors of the constraints is bounded. It is intended to show that this global condition can be replaced by a weaker local condition for almost all purposes. 2) The primal and the dual partitions are the result of classifying a given optimization problem and its dual as either inconsistent or bounded or unbounded, whereas the primal-dual partition is formed by the non-empty intersections of the elements of both partitions. The topological interior of these partitions are formed by those problems for which sufficiently small perturbations maintain the membership of the problem, i.e., the problems that are stable for the corresponding property. We propose to characterize the stable problems of the primal-dual partition without imposing any condition referring to the continuity of the analyzed problems and to any structure on the index set. 3) Finally, we intend to extend results about stability from to LSIP and CSIP to the abstract convex setting. Human resources are very important, so we propose to incorporate undergraduate students to initiate them in research. Moreover, three of the members of the research team will complete their graduate studies, two at Master level and one at Doctorate level.