向量变分不等式的间隙函数与误差界研究

项目名称： 向量变分不等式的间隙函数与误差界研究

项目编号： No.11426055

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 徐阳栋

作者单位： 重庆邮电大学

项目金额： 3万元

中文摘要： （向量）变分不等式的间隙函数与误差界研究是最优化理论的一个重要的研究方向。变分不等式的间隙函数与误差界的研究结果已经很漂亮，而向量变分不等式的间隙函数的研究还不完善，所得到的间隙函数的性质不够好；其误差界的研究才刚刚起步，所给的条件往往涉及到解集信息或者针对向量变分不等式的解集是一般集合，而应用到相应的变分不等式时解集却变成单点。本课题拟采用像空间分析工具与方法研究向量变分不等式的间隙函数，特别是具有可微性的间隙函数，在保证解集是一般集合以及不用解集信息的情况下，研究向量变分不等式的误差界，并将研究成果应用于具有广泛实际背景的多目标（向量）交通网络均衡问题中。本课题的研究不仅具有重要的理论意义，而且能够为经济系统、通讯系统和国防系统等领域中大量存在的网路均衡问题提供决策指导。

中文关键词： 向量变分不等式；向量平衡问题；间隙函数；误差界；向量交通网络均衡问题

英文摘要： The study on gap functions and error bounds for (vector) variational inequalities is an important research area of optimization theory. The research results on the gap functions and the error bounds for variational inequalities have been very beautiful, but the study on the gap functions for vector variational inequalities is not perfect, the properties of the gap function obtained are not well. The research on the error bounds for vector variational inequalities is just getting started, the conditions added frequently involve the solution set information, or although the solution sets of vector variational inequalities are the general sets, yet when being applied to the corresponding variational inequalities, the solution sets are singleton. Being planned to adopt the tools and methods in image space analysis, the project shall study the gap functions for vector variational inequalities, especially, differentiable gap functions, and on the conditions that the solution sets are the general sets and the assumptions do not involve the solution set information, shall study the error bounds for vector variational inequalities, in additional, shall apply the obtained results to multiobjective (vector) traffic network equilibrium problems with general actual background. The research of the project not only has importa

英文关键词： Vector variaitonal inequality；Vector equlibrium problem；Gap function；Error bound；Vector traffic network equilibrium problem