【作者】 应晶晶； 朱德通；

【Author】 Jing-Jing Ying~(1,*)De-Tong Zhu~(2,+) 1 Mathematics and Sciences College,Shanghai Normal University,Shanghai 200234,China 2 College of Business,Shanghai Normal University,Shanghai 200234,China

【机构】 上海师范大学数理学院； 上海师范大学商学院；

【摘要】 本文通过引入非单调投影梯度信赖域方法解决有界约束半光滑欠定方程组。基于简单有界约束非线性优化问题构建信赖子问题,半光滑高斯牛顿步在可行域投影得到投影高斯牛顿的试探步,获得新的搜索方向,结合非单调线搜索技术得到回代步,获得新的步长。在合理的条件下,证明算法具有全局和局部收敛性。最后,数值试验表明算法的可行性和有效性。更多还原

【Abstract】 In this paper,a gradient projection trust-region method with non-monotone line search technique is modified and extended for the solution of the underdetermined case subject to simple bounds.To compute trial steps,a search direction is introduced by projecting a semismooth Gauss-Newton -like step onto the feasible set.Combining the search direction with non-monotone model technique,a new accepted step is obtained at each iteration by the quadratic model.Global and local convergence properties are obtained under suitable assumptions.The numerical experiments are presented to explain feasibility and effectiveness of the algorithm.更多还原