Busca de Wolfe: Parˆâmetros Eficientes Obtidos Matematicamente

Abstract

Finding zeros of gradient a $n$-variables real function is a task which may be applied to solve problems of the speech recognition and machine translation. On Continuous Optimization, this task can be solved by using iterative methods which generates sequences that converge to a solution. Such methods must be computationally efficient. Line Search generally are used in iterative method in order to ensured a good computational efficiency. This Line Search finding step sizes for each iteration of the generated sequence for iterative method. Generally, these line search are defined by parameters that directly affect the numerical efficiency of the method used. Therefore, this is relevant for a mathematical investigation. The current literature has being not presented optimal parameters obtained mathematically. In this work, in order to find zeros of the gradient of an academic function, we mathematically determine a range of parameters for Wolfe's linear search. This range ensures more efficient step sizes when compared to other step sizes outside of the range. Our numerical study demonstrate the validity of the theoretical result obtained.