Convergencia de algoritmos de programación no lineal mediante mapeo cerrado
No Thumbnail Available
Date
2021
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
Universidad Nacional de Trujillo
Abstract
En los problemas de optimización no lineal la búsqueda de la solución muchas veces es complicada y los algoritmos que resuelven esta clase de problemas son métodos iterativos los cuales en cada iteración se aproximan a la solución estos métodos siempre deben estar acompañados de su análisis de convergencia. En este presente trabajo presentamos la demostración del Teorema de convergencia global de Zangwill para algoritmos de programación no lineal, mediante el uso de mapeo cerrado. La base de la demostración de convergencia es representar un algoritmo A como la composición de mapeos cerrados C y B, donde B encuentra alguna dirección de descenso y C encuentra el tamaño de paso ´optimo, si esta representación satisface con ciertas condiciones obtenemos la convergencia del algoritmo A. Además mostraremos la convergencia de 3 métodos de descenso por mapeo cerrado: método de la gradiente, método de Newton y Método de minimización a lo largo de direcciones independientes
Abstract In nonlinear optimization problems, the search for the solution is often complicated and the algorithms that solve this kind of problem are iterative methods which in each iteration approach the solution, these methods must always be accompanied by their convergence analysis. In this present work we present the proof of the Zangwill Global Convergence Theorem for nonlinear programming algorithms, through the use of closed mapping. The basis of the proof of convergence is to represent an algorithm A as the composition of closed mappings C and B, where B finds some direction of descent and C finds the optimal step size, if this representation satisfies with certain conditions we obtain the convergence of the algorithm A. We will also show the convergence of 3 methods of descent by closed mapping: the gradient method, Newton’s method and the minimization method along independent directions
Abstract In nonlinear optimization problems, the search for the solution is often complicated and the algorithms that solve this kind of problem are iterative methods which in each iteration approach the solution, these methods must always be accompanied by their convergence analysis. In this present work we present the proof of the Zangwill Global Convergence Theorem for nonlinear programming algorithms, through the use of closed mapping. The basis of the proof of convergence is to represent an algorithm A as the composition of closed mappings C and B, where B finds some direction of descent and C finds the optimal step size, if this representation satisfies with certain conditions we obtain the convergence of the algorithm A. We will also show the convergence of 3 methods of descent by closed mapping: the gradient method, Newton’s method and the minimization method along independent directions
Description
Keywords
Mapeo cerrado, Método de la gradiente, Método de Newton, Optimización no lineal