Applications, Algorithms and Theory of Mathematical Programming

非常有前途的数学规划技术 应用于医学诊断和预后， 一般的机器学习五年的经验与高度准确的 威斯康星州大学目前使用的乳腺癌诊断系统 医院，是借鉴发展线性规划为基础的预后 系统 求解大规模约束问题的并行算法 通过分配问题的成分， （约束、梯度或/和变量）。 每个处理器 对改变自己的问题负有全部责任 成分，同时允许其他成分在有限的范围内变化， 时尚. 处理器共享计算出的新信息， 并重复该过程。 初步算法原型 已经成功地测试了一些高并行效率上 公开可用的测试问题和重要的实际应用。 误差 边界是为可能不一致的不等式系统开发的， 方案和互补性问题。 这个新奇的想法 系统可能是不可解的，边界是有意义的， 系统是否可解。 在后一种情况下，它限制了距离 在所考虑的点和最小误差的集合之间， 系统的解决方案。 某机器的数学规划新方法 学习问题进行了研究。 特别是一个新的二次规划模型 神经网络中的级联架构正在研究中，事实也是如此 另一个是解决最大限度地减少 通过分离平面错误分类点。

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.