Computing semiparametric bounds on the expected payments of insurance instruments via column generation

It has been recently shown that numerical semiparametric bounds on the expected payoff of fi- nancial or actuarial instruments can be computed using semidefinite programming. However, this approach has practical limitations. Here we use column generation, a classical optimization technique, to address these limitations. From column generation, it follows that practical univari- ate semiparametric bounds can be found by solving a series of linear programs. In addition to moment information, the column generation approach allows the inclusion of extra information about the random variable; for instance, unimodality and continuity, as well as the construction of corresponding worst/best-case distributions in a simple way

Copositive certificates of non-negativity for polynomials on semialgebraic sets

A certificate of non-negativity is a way to write a given function so that its non-negativity becomes evident. Certificates of non-negativity are fundamental tools in optimization, and they underlie powerful algorithmic techniques for various types of optimization problems. We propose certificates of non-negativity of polynomials based on copositive polynomials. The certificates we obtain are valid for generic semialgebraic sets and have a fixed small degree, while commonly used sums-of-squares (SOS) certificates are guaranteed to be valid only for compact semialgebraic sets and could have large degree. Optimization over the cone of copositive polynomials is not tractable, but this cone has been well studied. The main benefit of our copositive certificates of non-negativity is their ability to translate results known exclusively for copositive polynomials to more general semialgebraic sets. In particular, we show how to use copositive polynomials to construct structured (e.g., sparse) certificates of non-negativity, even for unstructured semialgebraic sets. Last but not least, copositive certificates can be used to obtain not only hierarchies of tractable lower bounds, but also hierarchies of tractable upper bounds for polynomial optimization problems.Comment: 27 pages, 1 figur

Hipoplasia de la valva posterior de la válvula mitral y válvula aórtica bicúspide. Una muy rara asociación para encontrar en un paciente adulto

The congenital heart diseases are a diagnostic challenge for the clinician, particularly when they are presented in an adult. These types of anomalies that are observed in the mitral valve can be presented in isolated form or together with other heart defects. The case is presented of a patient with severe hypoplasia of the posterior mitral valve leaflet. This anomaly is, under normal conditions, fatal before birth or very symptomatic during childhood, and its delayed presentation is extremely rare and difficult to find in the adult. This the first case reported, not only in this country, but in the whole of South America. © 2018 Sociedad Colombiana de Cardiología y Cirugía Cardiovascula

On relaxations of the max kk-cut problem formulations

A tight continuous relaxation is a crucial factor in solving mixed integer formulations of many NP-hard combinatorial optimization problems. The (weighted) max $k$-cut problem is a fundamental combinatorial optimization problem with multiple notorious mixed integer optimization formulations. In this paper, we explore four existing mixed integer optimization formulations of the max $k$-cut problem. Specifically, we show that the continuous relaxation of a binary quadratic optimization formulation of the problem is: (i) stronger than the continuous relaxation of two mixed integer linear optimization formulations and (ii) at least as strong as the continuous relaxation of a mixed integer semidefinite optimization formulation. We also conduct a set of experiments on multiple sets of instances of the max $k$-cut problem using state-of-the-art solvers that empirically confirm the theoretical results in item (i). Furthermore, these numerical results illustrate the advances in the efficiency of global non-convex quadratic optimization solvers and more general mixed integer nonlinear optimization solvers. As a result, these solvers provide a promising option to solve combinatorial optimization problems. Our codes and data are available on GitHub

Gestión de la atención primaria de la salud en un contexto de mercado: análisis de caso en un hospital público de Bogotá, Colombia, 2008-2011

La política de salud de Bogotá (2004-2011) se orientó hacia la materialización del derecho a la salud a partir de la implementación de la estrategia de Atención Primaria en Salud, lo cual se realizó en abierta controversia con la política nacional basada en mecanismos de focalización y aseguramiento. Algunos de los hospitales públicos de la ciudad emprendieron procesos de transformación institucional para adoptar la nueva política sectorial. Con la intención de evidenciar la experiencia concreta de uno de estos hospitales se realizó un estudio de caso para reconocer los procesos involucrados en la gestión del modelo de Atención Primaria en Salud del Hospital del Sur en Bogotá entre los años 2008-2011, identificando aquellos factores que lo viabilizaron, así como los obstáculos, tensiones y contradicciones que se presentaron. Es así como se realizó una revisión documental, construcción de relatos y entrevistas semi-estructuradas con actores clave. Se describe el proceso de construcción del modelo, los dispositivos que facilitaron su desarrollo y las contradicciones emergentes en el intento de transformar la gestión de un hospital público desde una perspectiva del derecho a la salud