The Levenberg-Marquardt Algorithm For Solving Bound-Constrained Nonlinear Systems

We presents a Levenberg-Marquardt method for solving the bound-constrained nonlinear equation F(x)=0,x??,where C Rn is a nonempty and closed con-vex set,F is defined on an open set containing ? and continuously differentiable We construct a trial step which combines a projected Levenberg-Marquadrt step with a negative gradient direction adjusted by a scaling matrix.This trail step can not only ensure the reduction of the objective function,but also improve the convergence rate of the algorithm.The iterates generated by the method are feasible.The algorithm has global convergence.And the method is quadratically convergent under local error bounded condition on F.Numerical results show that the new algorithm works quite well.