多目标凸优化束方法子问题的对偶问题分析  

The dual problem analysis of bundle method subproblem for multiobjective convex optimization

作　　者：沈洁[1] 田淼 张俊男 胡盼 SHEN Jie;TIAN Miao;ZHANG Jun-nan;HU Pan(School of Mathematics,Liaoning Normal University,Dalian 116029,China)

机构地区：[1]辽宁师范大学数学学院,辽宁大连116029

出　　处：《吉林师范大学学报（自然科学版）》2018年第2期59-62,共4页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(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：多目标凸优化在众多领域中都有广泛应用,因此找到能够有效解决这一问题的方法尤为重要.利用改进函数将约束优化问题转化为无约束优化问题,借助惩罚思想构建近似模型,将相应子问题改写成二次规划子问题.最后通过求解其对偶问题,得到原子问题解的显式表达以及相关重要结论,这些结论对整个算法的收敛性分析起着重要作用.Multiobjective convex optimization is widely used in many fields,so it??s of great significance to find effective ways to solve it.Improved functions are used to turning constrained optimization problems into unconstrained optimization and approximate model is built with the help of penalty ideas,and the corresponding subproblem is rewritten into quadratic programming subproblem.Finally,by solving the dual problem,the explicit expression of the solution of the original subproblem and other relatively important conclusions are obtained.These conclusions play an essential role in the convergence analysis of the whole algorithm.

关 键 词：多目标凸优化 束方法 次梯度 对偶问题 

分 类 号：O221.2[理学—运筹学与控制论]