多目标凸规划迫近束方法二次规划子问题的研究  

On the study of quadratic subproblem of proximal bundle method for multiobjective programming

作　　者：沈洁[1] 张俊男 李函阳 胡盼 SHEN Jie , ZHANG Junnan , LI Hanyang , HU Pan(School of Mathematics, Liaoning Normal University, Dalian 11G029, Chin)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《辽宁师范大学学报（自然科学版）》2018年第2期4-7,共4页Journal of Liaoning Normal University:Natural Science Edition

基　　金：国家自然科学基金资助项目(11301246);辽宁省自然科学基金指导计划项目(20170540573);辽宁省教育厅科学技术研究项目(LF201783607)

摘　　要：在非光滑问题中,束方法展示出非常高的有效性.针对多目标凸规划,借助束方法试图寻找它的弱帕雷托最优解.利用目标函数和约束函数构造了一个改进函数,同时揭示了改进函数与原问题之间的关系.构建了改进函数的一个下近似模型,进一步通过求解二次规划子问题寻找下一个迭代点.利用Lagrange函数得出了原子问题最优解的显示表达.The bundle method shows very high efficiency in nonsmooth problems.For multiobjective convex programming problems,this paper attempts to find its weakly Pareto optimal solution with the aid of the bundle method.Firstly,an improved function is constructed by using the objective functions and the constraint functions.At the same time,the relationship between the improved function and the original problem is revealed.Then a lower approximation model of the improved function is constructed,and the next iteration point is generated by solving the quadratic programming subproblem.We use the Lagrange function to obtain the expression of optimal solution of the original subproblem.

关 键 词：非光滑 多目标凸优化 束方法 迭代子问题 

分 类 号：O221.2[理学—运筹学与控制论]