中文摘要：

作者与减少的射影的麻袋布联合建议一个仿射的可伸缩的修改坡度路径方法；为解决线性平等的非单调的内部回溯线搜索技术在变量上抑制了优化题目到界限。由采用限制矩阵的 QR 分解；处于潜水艇问题的减少的射影的麻袋布矩阵的 eigensystem 分解，作者形成仿射的可伸缩的修改坡度曲线的路径很容易。由使用内部回溯的线搜索技术，各重申换到严格的内部可行性的试用步。全球集中；建议算法的快本地 superlinear/quadratical 集中率在一些合理条件下面被建立。一个非单调的标准应该引起在一些性恶的盒子中加快集中进步。数字实验的结果被报导显示出建议算法的有效性。

英文摘要：

The authors propose an affine scaling modified gradient path method in association with reduced projective Hessian and nonmonotonic interior backtracking line search techniques for solving the linear equality constrained optimization subject to bounds on variables. By employing the QR decomposition of the constraint matrix and the eigensystem decomposition of reduced projective Hes- sian matrix in the subproblem, the authors form affine scaling modified gradient curvilinear path very easily. By using interior backtracking line search technique, each iterate switches to trial step of strict interior feasibility. The global convergence and fast local superlinear/quadratical convergence rates of the proposed algorithm are established under some reasonable conditions. A nonmonotonic criterion should bring about speeding up the convergence progress in some ill-conditioned cases. The results of numerical experiments are reported to show the effectiveness of the proposed algorithm.