Mathematical Sciences: Algorithms for Mathematical Programming

9414438 Goldfarb本研究的目标是开发、分析和实施用于解决数学规划问题的算法。这个项目的重点是单纯形算法、内点算法和结合内点和乘子惩罚方法的算法，特别强调在理论和实践中都是有效的算法。将开发专门用于网络流问题的算法，以及那些利用大规模并行计算机体系结构的算法。由于科学和工程中的许多问题可以被描述为大规模优化问题，因此，在该项目下开发有效的优化算法将对优化之外的领域产生影响，例如制造(生产计划和调度)、生物技术(蛋白质折叠)、民用基础设施(机队和机组人员调度和运输计划)、电信(网络设计和路线选择)以及优化领域本身。

9414438 Goldfarb The objectives of this research are the development, analysis, and implementation of algorithms for solving mathematical programming problems. The focus of this project is on simplex algorithms, interior point algorithms and algorithms that combine interior point and multiplier penalty approaches, with particular emphasis on algorithms that are efficient both in theory and in practice. Specialized algorithms for network flow problems and those that take advantage of the architecture of massively parallel computers will be developed. Since many problems in science and engineering can be formulated as large-scale optimization problems, the development of efficient optimization algorithms under this project will have an impact on fields outside of optimization such as manufacturing (production planning and scheduling), biotechnology (protein folding), civil infrastructure (fleet and crew scheduling and transportation planning), and telecommunications (network design and routing) as well as on the field of optimization itself.