New approximations for the cone of copositive matrices and its dual

• 成果类型: Article
• 署名作者: Lasserre, Jean B.
• 署名单位: Universite de Toulouse; Centre National de la Recherche Scientifique (CNRS); Universite de Toulouse
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-013-0632-5
• 发表日期: 2014
• 页码: 265-276
• 关键词: stability number; optimization; semidefinite; graph

摘要

We provide convergent hierarchies for the convex cone of copositive matrices and its dual , the cone of completely positive matrices. In both cases the corresponding hierarchy consists of nested spectrahedra and provide outer (resp. inner) approximations for (resp. for its dual ), thus complementing previous inner (resp. outer) approximations for (for ). In particular, both inner and outer approximations have a very simple interpretation. Finally, extension to -copositivity and -complete positivity for a closed convex cone , is straightforward.