Reportes Técnicos

Abstract: In this paper we propose a second–order method for solvinglinear compos-ite sparse optimization problemsconsisting of minimizing the sum of a differentiable(possibly nonconvex function) and a nondifferentiable convex term. The compositenondifferentiable convex penalizer is given by 1–norm of a matrix multiplied with thecoefficient vector. The algorithm that we propose for the case of the linear composite1–norm problem relies on the three main ingredients that power the OESOM algo-rithm [6]: the minimum norm subgradient, a projection step and, in particular, thesecond–order information associated to the nondifferentiable term. By extending thesedevices, we obtain a full second–order method for solving composite sparse optimiza-tion problems which includes a wide range of applications. For instance, problemsinvolving the minimization of a general class ofdifferential graph operatorscan besolved with the proposed algorithm. We present several computational experiments toshow the efficiency of our approach for different application examples.

Abstract: We consider the exact penalization of the incompressibility condition $div(u) =0$ for the velocity field of a Bingham fluid in terms of the $L1$–norm. This penalization procedure results in a nonsmooth optimization problem for which we propose an algorithm using generalized second–order information. Our method solves the resulting nonsmooth problem by considering the steepest descent direction and extra generalized second–order information associated to the nonsmooth term. This method has the advantage that the divergence-free property is enforced by the descent direction proposed by the method without the need of build-in divergence-free approximation schemes. Theinexact penalization approach, given by the $L2$–norm, is also considered in our discussionand comparison.

Abstract: This study combines statistical analysis and discrete optimization techniques to solve the problem of assigning patients to therapists for crisis intervention with a single tele-psychotherapy session. The statistical analysis showed that professionals and healthcare workers in contact with Covid–19 patients or with a confirmed diagnosis had a significant relationship with suicide risk, sadness, experiential avoidance, and perception of severity. This allowed categorizing patients according to their screening and grouping therapists according to their qualifications. A multi-periodic optimization model and a heuristic are proposed to find an adequate assignment of patients to therapists over time. The integer programming model was validated with real-world data, and its results were applied in a volunteer program in Ecuador. Keywords: Integer Programming, Logistic Regression, WLSMV, AAQ-II, Tele-Psychotherapy, Clinical Psychology, SARS–CoV2

Abstract: En este reporte presentamos el esquema variacional utilizado por el Centro de Modelización Matemática para estimar los diferentes parámetros y condiciones iniciales de los modelos de propagación del SARS-CoV-2 en Ecuador, en presencia de incertidumbre en los datos. Esta estimación permite realizar actualizaciones periódicas del número efectivo de reproducción de la epidemia, así como proyecciones a corto plazo de su propagación

Abstract: Ante la inminente llegada de la pandemia de la enfermedad Covid 19, conocida como Coronavirus, al territorio ecuatoriano, el Centro de Modelización Matemática de la Escuela Politécnica Nacional conformó un equipo de trabajo especializado para modelizar y simular la propagación del SARS-CoV-2 (virus causante de la enfermedad), bajo varios escenarios de política pública aplicados a la contención del mismo. En este reporte explicamos los modelos utilizados, las simulaciones obtenidas y las recomendaciones para mejorar los modelos y, sobre todo, para el diseño de políticas públicas que ayuden a minimizar los efectos negativos de la pandemia en la población, mientras se desarrollan las actividades productivas esenciales para el país.