Fuzzy Levenberg Marquart optimization algorithm with inexact line search technique to solve imprecisely defined nonlinear unconstrained optimization problems

This paper proposes a fuzzy inexact Levenberg-Marquardt optimization (FILMO) algorithm with a descent direction to handle the nonlinear systems influenced by the uncertain parameters. The main feature of this proposed inexact algorithm is to use the Armijo-type step size search approach via an uncertain environment. The level of inexactness search direction is controlled through the descent direction of the merit function. We establish the convergence analysis of the FILMO algorithm under the assumption of local error bound. Then, the global convergence of the FILMO algorithm is described. The FILMO algorithm is constructed using fuzzy parameters with an Armijo-type step size approach. Numerical examples are illustrated to investigate the effectiveness and efficiency of the algorithm. Then, the comparison is done with a previously existing conjugate gradient modified Fletcher-Reeves method and fuzzy inner outer direct search (FIODS) method. Furthermore, to quantify the uncertainties and sensitivity of the system, fuzzy and fully fuzzy systems are investigated through a case study.