Perfect Copositive Matrices

完美共积矩阵

• 批准号: 467575515
• 负责人: Professor Dr. Achill Schürmann
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/467575515?language=en
• 关键词: Perfect; Copositive; Matrices

In this project we develop a theory of perfect copositive matrices. These matrices can be used, for example, to discretize the convex cone of copositive matrices in a systematic way. This results in possible applications in copositive optimization, such as the algorithmic calculation of rational certificates for completely positive matrices. A central component of our project — and important for algorithmic applications of the new theory — is the investigation of the neighborhood graph of perfect copositive matrices. This graph appears as an edge graph of a polyhedral surface, whose facets are determined by minimal vectors of copositive matrices. For the algorithmic treatment of the neighborhood graph it is therefore essential to compute minimal vectors of copositive matrices. For this important task new approaches are developed and tested. These new algorithms for determining minimal vectors themselves have the potential for interesting future applications.As part of the project, we will develop various implementations of algorithms and compare them extensively with known approaches. Towards the end we aim to publish software that is easy to use, together with an associated data set of test instances for future research.

在这个项目中，我们开发了一种完美的共同材料的理论。这些物品可用于以系统的方式离散共同材料的凸锥。这导致可能在共同优化中应用，例如完全积极物质的理性证书的算法计算。我们项目的核心组成部分 - 对于新理论的算法应用至关重要 - 是完美共同材料的邻里图的投资。该图显示为多面体表面的边缘图，其方面由共同材料的最小向量确定。因此，对于邻里图的算法处理，必须计算共同材料的最小载体。对于这项重要任务，开发和测试了新方法。这些新算法用于确定最小媒介本身具有有趣的未来应用的潜力。作为该项目的一部分，我们将开发各种算法实现，并将其与已知方法进行广泛的比较。最后，我们旨在发布易于使用的软件，以及相关的数据集，以供将来的研究。