求解双目标规划的近似邻近外梯度算法  

An approximate proximal extragradient algorithm for double objective optimization

作　　者：高雷阜[1] 魏帅[1] 

机构地区：[1]辽宁工程技术大学理学院,辽宁阜新123000

出　　处：《辽宁工程技术大学学报（自然科学版）》2014年第4期552-555,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：国家自然基金青年基金资助项目(G010303);辽宁省教育厅基金资助项目(L2012105)

摘　　要：为解决双目标规划问题的常规解法受预先设定的权重的影响,而影响其结果准确性的问题,提出了双目标规划问题的近似邻近外梯度算法.结果表明:将双目标规划问题等价变形为变分不等式,在求解变分不等式子问题的基础之上,用半空间投影构造迭代步,避开了对权重的设定,证明了算法的全局收敛性.实例分析进一步验证算法的可行性与有效性.In order to overcome the problem that the conventional method for double objective programming problems is based on the pre-determined weight which often affects the accuracy of the results, this study presented an approximate proximal extragradient algorithm. Research concluded that by equivalently deforming the double objective programming to a variational inequality problem, then based on the variational inequality sub-problem, constructed a h-ilf-space projection iteration step and dodge the pre-determined weight, while ensure its results without losing accuracy, further demonstrated the global convergence of the algorithm.

关 键 词：双目标规划 变分不等式 半空间投影 近似邻近外梯度算法 全局收敛 随机步长 灵活性 准确性 

分 类 号：O221.2[理学—运筹学与控制论]