Interior-Point Methods in Artificial Neural Networks

该项目将研究将内点技术应用于神经网络学习算法的好处。私家侦探将试图证明，通过使用内点法的工具，神经网络算法如反向传播算法可以通过优化给定的学习方法来提高学习时间和解的质量。作为一项介绍性研究，本提案将通过研究分析中心的方法来研究BP对学习的影响（Huard 1967, Sonnevend 1985, Renegar 1989）。Trafalis（1989）、Abhyankar、Morin和Trafalis（1990）针对多目标优化问题开发并研究了类似的方法。提出的研究将按照三部分计划进行：(1)考虑分段线性凸激活函数。然后将研究结果推广到更一般的激活函数（例如s型函数）；(2)设计、实现和计算测试在研究第一阶段开发的学习算法；(3)检验已开发的与癌症诊断医学应用相关的视觉问题学习规律。

This project will investigate the benefits of applying interior point techniques to learning algorithms in neural networks. The P.I. will attempt to show that by using the tools of interior point methods, a neural network algorithm such as back propagation can be improved both in learning time and quality of solution by optimizing the given methods of learning. As an introductory study, this proposal will investigate the effects on learning in BP by studying a method of analytical centers (Huard 1967, Sonnevend 1985, Renegar 1989). A similar approach was developed and investigated by Trafalis (1989), Abhyankar, Morin and Trafalis (1990) for multiobjective optimization problems. The proposed research would be conducted according to a three-part plan: (1) To consider piecewise linear convex activation functions. The findings of the research will then be generalized to cover more general activation functions (e.g. sigmoid functions); (2) To design, implement and computationally test the learning algorithms which were developed in phase one of the research; (3) To test the developed learning laws in vision problems related to medical applications in cancer diagnosis.