Sparse Matrix Algorithms and their Application to Dual Active Set Techniques in Optimization

稀疏矩阵算法及其在优化中双主动集技术的应用

• 批准号: 0203270
• 负责人: Timothy Davis
• 金额: $ 51万
• 依托单位: University of Florida
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2007-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0203270&HistoricalAwards=false
• 关键词: Sparse; Matrix; Algorithms; their; Application

Davis, TimothyUniversity of Florida0203270The focus of this project is the development of innovative library-quality software and under-lying mathematics for dual active set techniques in optimization.The dual active set algorithm(DASA)was .rst introduced in the context of state constrained control problems,and later in thecontext of constrained mathematical programs.For linear or quadratic programming,each step ofthe algorithm is equivalent to solving a linear system of equations,and in successive steps,thereis a small rank change in the matrix corresponding to the change in the active set.Numericalexperience has shown that the dual active set framework is an extremely e .cient approach forsolving some broad classes of optimization problems,including problems in optimal control andquadratic network optimization.A version of the algorithm targeted to linear programming hasalready solved some LPs that other state-of-the-art packages are unable to solve.We will developa variety of sparse matrix techniques,which have broad applicability,and which provide,in par-ticular,the numerical foundation for DASA.Each technique will be developed into library-qualitysoftware and made widely available.These include:

戴维斯（Davis），佛罗里达0203270的蒂莫西亚夫斯（Timothyuniversity），该项目的重点是开发创新的图书馆质量软件和较低的数学数学，用于优化的双重主动设置技术。双重活动集算法（DASA）在每个介绍的情况下是在状态约束控制问题的上下文中进行的。算法等同于求解方程式系统，并且在连续的步骤中，矩阵中的等级变化很小，与活动集合的变化相对应。NumericalialicalExperiention表明，双活动设置框架是一种极为e的方法，可以实现一些广泛的问题，包括优化的问题，包括最佳控制和序列化的目标。解决了其他最先进的软件包无法解决的LP。我们将开发各种稀疏矩阵技术，这些技术具有广泛的适用性，并且以较低的方式提供了DASA的数值基础。每个技术将开发为库 - Qualitysoftware，并广泛可用。