Optimierung über gemischt-ganzzahligen Polynomprogramme

混合整数多项式程序的优化

• 批准号: 5362666
• 负责人: Professor Dr. Robert Weismantel
• 金额: --
• 依托单位: Department of Mathematics
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2002
• 资助国家: 德国
• 起止时间: 2001-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5362666?language=en
• 关键词: Optimierung; ber; gemischt; ganzzahligen; Polynomprogramme

This research project is devoted to the study of algorithms for optimizing over mixed integer poloynomial programs. Mixed integer polynomial programs are a significant generalization of linear integer programs in the sense that the constraints of a polynomial program are polynomial inequalities or equations in the variables. The algorithms to be designed will be based on generalizations of various results from the theory of linear integer programming and will try to follow the basic algorithmic streamline in integer programming. More precisely, we plan to develop some basic theory for designing dual type methods, primal type methods, and finally a primal dual method for mixed integer polynomial programs. As a result we expect various theoretical results about the structure of the set of feasible solutions that will be used in our algorithms. We intend to test these algorithmic ideas on polynomial systems arising from questions in chemical engineering that are investigated in the research projects TP3, TP4 and TP5. Indeed these applications motivate this project.

本课题主要研究混合整数多项式规划的优化算法。混合整数多项式规划是线性整数规划的一个重要推广，因为多项式规划的约束条件是变量中的多项式不等式或方程。所设计的算法将基于线性整数规划理论的各种结果的概括，并将尝试遵循整数规划中的基本算法流线。更确切地说，我们计划发展一些设计对偶型方法的基本理论，原始类型方法，最后是混合整数多项式规划的原始对偶方法。因此，我们期望关于可行解集结构的各种理论结果将用于我们的算法中。我们打算在研究项目TP3， TP4和TP5中研究的化学工程问题中产生的多项式系统上测试这些算法思想。实际上，这些应用程序激发了这个项目。

项目成果

FPTAS for optimizing polynomials over the mixed-integer points of polytopes in fixed dimension

• DOI: 10.1007/s10107-007-0175-8
• 发表时间: 2007-06
• 期刊: Mathematical Programming
• 影响因子: 2.7
• 作者: J. D. Loera;R. Hemmecke;M. Köppe;R. Weismantel

Nonlinear Matroid Optimization and Experimental Design

非线性拟阵优化和实验设计

• DOI: 10.1137/070696465
• 发表时间: 2008
• 期刊: ArXiv
• 作者: Y. Berstein;S. Onn;H. Maruri;H. Wynn;E. Riccomagno;R. Weismantel
• 通讯作者: R. Weismantel

Integer Polynomial Optimization in Fixed Dimension

• DOI: 10.1287/moor.1050.0169
• 发表时间: 2004-10
• 期刊: Math. Oper. Res.
• 作者: J. D. Loera;R. Hemmecke;M. Köppe;R. Weismantel

Convex integer maximization via Graver bases

通过 Graver 基实现凸整数最大化

• DOI: 10.1016/j.jpaa.2008.11.033
• 发表时间: 2009
• 期刊: Journal of Pure and Applied Algebra
• 影响因子: 0.8
• 作者: J. De Loera;R. Hemmecke;Shmul Onn;U. G. Rothblum;R. Weismantel
• 通讯作者: R. Weismantel

Mod-2 Cuts Generation Yields the Convex Hull of Bounded Integer Feasible Sets

• DOI: 10.1137/04061831x
• 发表时间: 2006-12
• 期刊: SIAM J. Discret. Math.
• 作者: C. Gentile;P. Ventura;R. Weismantel