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

这个项目的重点是开发创新的图书馆质量软件和优化对偶活动集技术的基础数学。双活动集算法（DASA）。在状态约束控制问题的背景下引入了RST，后来在约束数学规划的背景下引入了RST。对于线性或二次规划，算法的每一步都相当于求解一个线性方程组，在连续的步骤中，矩阵中有一个小的秩变化对应于活动集的变化。数值经验表明，对偶活动集框架是一种极值框架。用客户的方法来解决一些广泛的优化问题，包括最优控制和二次网络优化问题。针对线性规划的算法版本已经解决了一些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，特别是为DASA提供数值基础。每一种技术都将被开发成图书馆级的软件，并广泛使用。这些包括:

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: