有界约束非线性方程组的仿射尺度内点信赖域方法

提供了仿射信赖域策略结合非单调线搜索算法解有界约束非线性方程组．基于简单有界约束的非线性优化问题构建信赖域子问题，但所用的最小仿射尺度比Coleman和Li所用的仿射尺度更为一般．在合理的条件下，文中提供的最小仿射尺度，在没有严格互补假设条件下，可给出更强的全局收敛性结果．引入非单调技术能克服高度非线性的病态问题．

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 minimumscaling.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.