The geometry of SDP-exactness in quadratic optimization

• 成果类型: Article
• 署名作者: Cifuentes, Diego; Harris, Corey; Sturmfels, Bernd
• 署名单位: Massachusetts Institute of Technology (MIT); University of Oslo; University of California System; University of California Berkeley
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-019-01399-8
• 发表日期: 2020
• 页码: 399-428
• 关键词: algebraic degree; cut

摘要

Consider the problem of minimizing a quadratic objective subject to quadratic equations. We study the semialgebraic region of objective functions for which this problem is solved by its semidefinite relaxation. For the Euclidean distance problem, this is a bundle of spectrahedral shadows surrounding the given variety. We characterize the algebraic boundary of this region and we derive a formula for its degree.