Cette thèse porte sur l’étude des méthodes inertielles pour résoudre les problèmes de minimisation convexe structurés. Depuis les premiers travaux de Polyak et Nesterov, ces méthodes sont devenues très populaires, grâce à leurs effets d’accélération. Dans ce travail, on étudie une famille d’algorithmes de gradient proximal inertiel de type Nesterov avec un choix spécifique de suites de sur-relaxation. Les différentes propriétés de convergence de cette famille d’algorithmes sont présentées d’une manière unifiée, en fonction du paramètre de sur-relaxation. En outre, on étudie ces propriétés, dans le cas des fonctions lisses vérifiant des hypothèses géométriques supplémentaires, comme la condition de croissance (ou condition de Łojasiewicz). On montre qu’en combinant cette condition de croissance avec une condition de planéité (flatness) sur la géométrie de la fonction minimisante, on obtient de nouveaux taux de convergence. La stratégie adoptée ici, utilise des analogies du continu vers le discret, en passant des systèmes dynamiques continus en temps à des schémas discrets. En particulier, la famille d’algorithmes inertiels qui nous intéresse, peut être identifiée comme un schéma aux différences finies d’une équation/inclusion différentielle. Cette approche donne les grandes lignes d’une façon de transposer les différents résultats et leurs démonstrations du continu au discret. Cela ouvre la voie à de nouveaux schémas inertiels possibles, issus du même système dynamique. / This Thesis focuses on the study of inertial methods for solving composite convex minimization problems. Since the early works of Polyak and Nesterov, inertial methods become very popular, thanks to their acceleration effects. Here, we study a family of Nesterov-type inertial proximalgradient algorithms with a particular over-relaxation sequence. We give a unified presentation about the different convergence properties of this family of algorithms, depending on the over-relaxation parameter. In addition we addressing this issue, in the case of a smooth function with additional geometrical structure, such as the growth (or Łojasiewicz) condition. We show that by combining growth condition and a flatness-type condition on the geometry of the minimizing function, we are able to obtain some new convergence rates. Our analysis follows a continuous-to-discrete trail, passing from continuous-on time-dynamical systems to discrete schemes. In particular the family of inertial algorithms that interest us, can be identified as a finite difference scheme of a differential equation/inclusion. This approach provides a useful guideline, which permits to transpose the different results and their proofs from the continuous system to the discrete one. This opens the way for new possible inertial schemes, derived by the same dynamical system.

Interface balance laws are derived to describe transport across a phase interface. This is used to derive generalized conditions for phase nucleation and growth, valid even for solids with inhomogeneous surface stress.<div><br></div><div>An explicit interface tracking approach called Enriched Isogeometric Analysis (EIGA) is used to simulate phase evolution. Algebraic level sets are used as a measure of distance and for point projection, both necessary operations in EIGA. Algebraic level sets are observed to often fail for surfaces. Rectification measures are developed to make algebraic level sets more robust and applicable for general surfaces. The proposed methods are demonstrated on electromigration problems. The simulations are validated by modeling electromigration experiments conducted on Cu-TiN line structures.</div><div><br></div><div>To model topological changes, common in phase evolution problems, Boolean operations are performed on the algebraic level sets using R-functions. This is demonstrated on electromigration simulations on solids with multiple voids, and on a bubble coalescence problem. </div>

Objetivo: Determinar el comportamiento del Control de Crecimiento y Desarrollo en niños nacidos en un centro de salud de Chiclayo periodo 2020-2022. Método: Estudio cuantitativo, diseño no experimental, descriptivo, transversal y retrospectivo, se basó en los criterios de rigor científico: validez, objetividad y los principios éticos. La población estuvo constituida por 311 historias clínicas de niños nacidos en los años 2020, 2021 y 2022 del Centro de Salud José Leonardo Ortiz, siendo la muestra final de 173 historias clínicas y se obtuvo mediante el muestreo no probabilístico por conveniencia. Se utilizó como instrumento una ficha de recolección según la Norma Técnica para el Control del Niño, que recogió ciertas características: datos generales sobre el niño, madre y padre; número de controles de crecimiento y desarrollo; condición de crecimiento y estado nutricional; y el diagnóstico del desarrollo Psicomotor. El procesamiento y análisis de la información se realizó en hojas de Excel 2016 y en el programa estadístico SPSS versión 22 a través de frecuencias absolutas y relativas. Resultados: El 58.3% de recién nacidos tuvieron 4 controles, el 37,8% de los niños tienen condición de crecimiento adecuado y el 36,9% obtuvo un desarrollo psicomotor normal. Conclusiones: La mitad de los recién nacidos, menos de la octava parte de los niños menores de 1 año y muy pocos niños de 1 año tienen los controles recomendados según edad, la cifra es preocupante porque puede repercutir en la detección temprana de alteraciones o trastornos tanto en el crecimiento como en el desarrollo. / Objective: Determine the behavior of Growth and Development Control in children born in a health center in Chiclayo period 2020-2022. Method: Quantitative study, non-experimental, descriptive, cross-sectional and retrospective design, was based on the rigor criteria scientific: validity, objectivity and ethical principles. The population was made up of 311 medical records of children born in the years 2020, 2021 and 2022 from the José Health Center Leonardo Ortiz, being the final sample of 173 medical records and was obtained through the non-probabilistic convenience sampling. A collection form was used as an instrument according to the Technical Standard for Child Control, which collected certain characteristics: general data about the child, mother and father; number of controls growth and development; growth condition and nutritional status; and the diagnosis of Psychomotor development. The processing and analysis of the information was carried out in Excel 2016 sheets and in the statistical program SPSS version 22 through absolute and relative frequencies. Results: 58.3% of newborns had 4 controls, 37.8% of children had adequate growth conditions and 36.9% obtained normal psychomotor development. Conclusions: Half of newborns, less than an eighth of children under 1 year of age and very few 1-year-old children have the recommended controls according to age, the figure is worrying because it can have an impact on the early detection of alterations or disorders both in growth and development.