The trust region subproblem with non-intersecting linear constraints

• 成果类型: Article
• 署名作者: Burer, Samuel; Yang, Boshi
• 署名单位: University of Iowa; University of Iowa
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-014-0749-1
• 发表日期: 2015
• 页码: 253-264
• 关键词: minimization

摘要

This paper studies an extended trust region subproblem (eTRS) in which the trust region intersects the unit ball with linear inequality constraints. When , or and the linear constraints are parallel, it is known that the eTRS optimal value equals the optimal value of a particular convex relaxation, which is solvable in polynomial time. However, it is also known that, when and at least two of the linear constraints intersect within the ball, i.e., some feasible point of the eTRS satisfies both linear constraints at equality, then the same convex relaxation may admit a gap with eTRS. This paper shows that the convex relaxation has no gap for arbitrary as long as the linear constraints are non-intersecting.