Convexity in real algebraic geometry

实代数几何中的凸性

• 批准号: 241225335
• 负责人: Professor Dr. Daniel Plaumann
• 金额: --
• 依托单位: Lehrstuhl VI: Algebra
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2013
• 资助国家: 德国
• 起止时间: 2012-12-31 至 2016-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/241225335?language=en
• 关键词: Convexity; real; algebraic; geometry

In this project, problems from convexity and from convex and polynomial optimisation are studied with specific methods from real algebraic geometry. This concerns fundamental questions arising from applications in optimisation (in particular semidefinite programming and positive polynomials), but also the classical geometry of curves and surfaces and their higher dimensional analogues. Two aspects that have received a lot of attention in recent years concern the representation of real polynomials by determinants and the description of convex sets by linear matrix inequalities.

在这个项目中，从凸性和凸和多项式优化的问题进行了研究与具体的方法从真实的代数几何。这涉及的基本问题所产生的应用程序在优化（特别是半定规划和正多项式），但也经典几何的曲线和曲面及其高维类似物。真实的多项式的行列式表示和凸集的线性矩阵不等式表示是近年来得到广泛关注的两个方面。

项目成果

Determinantal representations of hyperbolic curves via polynomial homotopy continuation

通过多项式同伦延拓的双曲曲线的行列式表示

• DOI: 10.1090/mcom/3194
• 发表时间: 2017
• 期刊: Math. Comput.
• 作者: Leykin;Plaumann;Daniel
• 通讯作者: Daniel

Gram Spectrahedra.

革兰氏谱面体

• DOI: 10.1090/conm/697/14047
• 发表时间: 2017
• 期刊: arXiv: Algebraic Geometry
• 作者: Plaumann;Daniel;Rainer;Vinzant;Cynthia
• 通讯作者: Cynthia

Symbolic computation in hyperbolic programming

双曲规划中的符号计算

• DOI: 10.1142/s021949881850192x
• 发表时间: 2018
• 期刊: Journal of Algebra and Its Applications
• 影响因子: 0.8
• 作者: Simone;Plaumann;Daniel
• 通讯作者: Daniel