A fast eigenvalue approach for solving the trust region subproblem with an additional linear inequality

被引：0
作者：
M. Salahi
A. Taati
机构：
[1] University of Guilan,Faculty of Mathematical Sciences
来源：
Computational and Applied Mathematics | 2018年 / 37卷
关键词：
Extended trust region subproblem; Lagrangian dual; Eigenvalue problem; Relaxation; 90C26; 90C22; 65F15;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study the extended trust region subproblem (eTRS) in which the trust region intersects the Euclidean ball with a single linear inequality constraint. By reformulating the Lagrangian dual of eTRS as a two-parameter linear eigenvalue problem, we state a necessary and sufficient condition for its strong duality in terms of an optimal solution of a linearly constrained bivariate concave maximization problem. This results in an efficient algorithm for solving eTRS of large size whenever the strong duality is detected. Finally, some numerical experiments are given to show the effectiveness of the proposed method.
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页码：329 / 347
页数：18
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