A One-Parameter Filled Function Method Applied to Nonlinear Equations

For box-constrained smooth system of nonlinear equations, a novel filled function with one parameter is derived, its properties are investigated, and an associated filled function algorithm is presented. By converting the nonlinear equations into an equivalent global minimization problem and then applying the proposed filled function algorithm to this optimization problem, we can identify the root of the nonlinear equations. For illustration, two test problems are utilized to demonstrate the efficiency of the proposed scheme. Preliminary numerical results show that our filled function method can effectively solve the system of nonlinear equations.