An affine-scaling trust-region method with interior backtracking technique for bound-constrained nonlinear equations

We develop an affine scaling trust region algorithm in association with the nonmonotone interior backtracking line technique for solving smooth nonlinear equations subject to bounds on variables.The trust region subproblem is defined by minimizing a squared Eudidean norm of linear model with a new affine matrix called minimum-scaling. Under a reasonable assumption of this new affine-scaling matrix,we stress that the minimum-scaling has some additional properties that allow us to prove stronger global convergence results without nondegenerate property than those about the Coleman-Li-scaling.The nonmonotonic criterion is used to speed up the convergence progress in the contours of objective function with large curvature.