Interior-Point Methods in Artificial Neural Networks

这个项目将调查将内点技术应用于神经网络中的学习算法的好处。P.I.将试图通过使用内点方法的工具来证明，一种神经网络算法，如反向传播算法，可以通过优化给定的参数，在学习时间和解的质量方面得到改善学习方法。作为一个介绍性研究，这项建议将通过研究分析中心的方法来调查BP学习的影响(Huard 1967，宋内文，1985年，雷尼格·)。特拉法里斯(1989)，Abhyankar，Morin和Trafais(1990)的多目标优化问题。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，研究结果将被推广到更一般的激活函数(例如，Sigmoid函数)；(2)对研究第一阶段开发的学习算法进行设计、实现和计算测试；(3)在癌症诊断中与医学应用相关的视觉问题上检验所开发的学习规律。

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.