Extensions of Fibonacci Search Technique for One Dimensional Interval Optimization Problem

Abstract

Abstract Fibonacci Search Technique is one of the familiar iterative methods for solving one dimensional unconstrained optimization problem with highly non-linear/non-differentiable objective function. However, sometimes objective function becomes inexact/imprecise in nature due to the uncertainty. To deal with such imprecise problem, present article focuses on an extension of Fibonacci Search technique whose algorithm is developed based on interval order relations. In this work, first of all, two different types of optimizers (maximizer/minimizer) viz., c-L optimizer, c-r optimizer, of an interval valued function are introduced based on different order relations. After that a result regarding the relation between said optimizers are established. Then, Fibonacci search type algorithms are developed for all types of optimizers. Finally, the said algorithms are illustrated with a number of numerical examples.