Applications, Algorithms and Theory of Mathematical Programming

数学规划的应用、算法和理论

• 批准号: 9322479
• 负责人: Olvi Mangasarian
• 金额: $ 29.63万
• 依托单位: University of Wisconsin-Madison
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-09-01 至 1999-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9322479&HistoricalAwards=false
• 关键词: Applications; Algorithms; Theory; Mathematical; Programming

Highly promising mathematical programming techniques applied to medical diagnosis and prognosis as well as to machine learning in general. Five years of experience with a highly accurate system for breast cancer diagnosis, in current use at University of Wisconsin Hospitals, is drawn upon to develop a linear-programming-based prognostic system. Parallel algorithms for the solution of large-scale constrained optimization problems are developed, by distributing ingredients of the problem (constraints, gradients, or/and variables) among parallel processors. Each processor has complete responsibility for varying its own problem ingredients, while allowing the other ingredients to vary in a restricted fashion. The processors share new information computed, then a fast synchronization is performed and the process is repeated. Preliminary algorithm prototypes have been tested successfully with some high parallelization efficiency on publicly available test problems and significant real-world applications. Error bounds are developed for possibly inconsistent systems of inequalities, programs and complementarity problems. The novel idea here is that the system may be unsolvable, and the bounds are meaningful whether the system is solvable or not. In the latter case, it bounds the distance between the point under consideration, and the set of least error solutions of the system. New mathematical programming approaches to some machine learning problems are studied. In particular a new quadratic programming model for a cascade architecture in neural networks is being studied, as is another one for the inherently difficult problem of minimizing the number of misclassified points by a separating plane.

非常有前途的数学规划技术应用于医学诊断和预后以及一般的机器学习。5年的经验，高度准确的乳腺癌诊断系统，目前在威斯康星大学医院使用，借鉴开发基于线性规划的预后系统。通过在并行处理器之间分配问题的成分（约束、梯度或/和变量），开发了用于解决大规模约束优化问题的并行算法。每个处理器都有责任改变自己的问题成分，同时允许其他成分以有限的方式改变。处理器共享计算的新信息，然后执行快速同步并重复该过程。初步的算法原型已经在公开可用的测试问题和重要的实际应用中成功地测试了一些高并行化效率。给出了可能不一致的不等式、规划和互补问题系统的误差界。这里的新颖思想是系统可能是不可解的，无论系统是否可解，边界都是有意义的。在后一种情况下，它限定了所考虑的点与系统最小误差解集之间的距离。研究了一些机器学习问题的新的数学规划方法。本文特别研究了一种新的神经网络级联结构的二次规划模型，以及另一种利用分离平面最小化错误分类点数量的固有难题。