A copositive formulation for the stability number of infinite graphs

• 成果类型: Article
• 署名作者: Dobre, Cristian; Duer, Mirjam; Frerick, Leonhard; Vallentin, Frank
• 署名单位: Wageningen University & Research; Universitat Trier; University of Cologne
• 刊物名称: MATHEMATICAL PROGRAMMING
• ISSN/ISSBN: 0025-5610
• DOI: 10.1007/s10107-015-0974-2
• 发表日期: 2016
• 页码: 65-83
• 关键词: quadratic optimization problems

摘要

In the last decade, copositive formulations have been proposed for a variety of combinatorial optimization problems, for example the stability number (independence number). In this paper, we generalize this approach to infinite graphs and show that the stability number of an infinite graph is the optimal solution of some infinite-dimensional copositive program. For this we develop a duality theory between the primal convex cone of copositive kernels and the dual convex cone of completely positive measures. We determine the extreme rays of the latter cone, and we illustrate this theory with the help of the kissing number problem.