项目名称: 交集上变分不等式的神经网络模型及应用研究
项目编号: No.61273311
项目类型: 面上项目
立项/批准年度: 2013
项目学科: 自动化技术、计算机技术
项目作者: 高兴宝
作者单位: 陕西师范大学
项目金额: 80万元
中文摘要: 利用动力系统和微分包含, 本项目将根据问题的内在特性, 分类设计能求解定义于闭集的交集上的变分不等式及其约束问题的神经网络模型, 包括连续时间神经网络、具有时滞的神经网络和适合于集值映射的不连续神经网络模型等;利用优化技巧构造恰当的能量函数, 分析模型的动态行为, 并给出易于验证的稳定性条件, 使新模型结构更简单、规模更小、收敛性能更理想且不需要计算交集上的投影. 其次, 针对图像处理和统计与机器学习等领域中出现的许多优化问题, 将基于问题的形式和特点, 通过适当地转化并应用设计求解交集上变分不等式模型的思路, 分类设计能求解它们的结构简单、规模小且不含罚参数的各种神经网络;定义恰当的能量函数, 研究新模型的稳定性和收敛性. 其意义在于适合硬件实现的神经网络不仅能实时求解许多实际问题, 而且它们的离散实现能以较小的计算量提供问题的较好解, 并为建立和理解数值稳定的算法提供理论基础.
中文关键词: 变分不等式;优化问题;神经网络;动态行为;算法
英文摘要: Using the theory of dynamical system and differential inclusion, this project will design the effective neural-network models for solving variational inequalities and their constrained problems defined on the intersection of the closed sets according to the inherent properties of the considered problems, respectively. These models include continuous-time neural networks, the ones with delays, discontinuous ones for the set-valued mapping and so on. Meanwhile, a suitable energy function is defined to analyze the dynamical behavior for each model by using optimization methods, and some easily checked stability conditions will be provided such that each model has very simpler structure, smaller size, better convergence performance and no requirement of computing directly the projection on the intersection of the closed sets. Moreover, based on the forms and the properties of the optimization problems in the fields of image processing, statistics, machine learning and so on, this project will also design several kinds of the neural-network models with simple structure, small size and no penalty parameter for them, and construct the energy functions to study their stability and convergence by using the suitable transformation and the idea to develop the models for variational inequality defined on the intersection of
英文关键词: Variational inequality;optimization problem;neural network;dynamical behavior;algorithm