Hybrid conjugate gradient method for solving fuzzy nonlinear equations

Fuzzy nonlinear equation (FNLE) plays an important role in many fields, including mathematics, engineering, statistics and so on. How to solve its numerical solution is an interesting problem. A hybrid conjugate gradient algorithm (HCGA) was proposed for solving FNLE. First, the parametric form of the equation was translated into an equivalent unconstrained optimization problem (UOP). Then, HCGA was applied to solve the corresponding optimization problem. Convergence of the algorithm was proved. Finally, numerical examples were given to illustrate the efficencies of HCGA. The comparative study shows that HCGA for solving FNLE is superior to the existent steepest descent algorithm (SDA) in terms of convergence and the numbers of iteration.