水平束方法子问题的求解研究  

Study on Subproblem of the Level Bundle Method

作　　者：沈洁[1] 赵睿[1] 高亚丽[1] 

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）》2017年第2期54-57,共4页Journal of Jilin Normal University:Natural Science Edition

基　　金：国家自然科学基金项目(11301246)

摘　　要：非光滑优化问题是最优化理论与方法中一个重要分支,相应的各种求解方法一直以来都是优化理论研究的重点.首先对解决非光滑优化问题的一种有效方法-束方法,进行了简单阐述,又对其中一种典型方法-水平束方法进行了详细研究.该方法利用水平集作为约束构造产生下一个迭代点的子问题,通过构建子问题的Lagrangian函数以及求解其对偶规划,得出原子问题最优解的显式表达.最后根据子问题的最优性条件和对偶问题得出两个在整体算法的收敛性分析中占有重要地位的结论.Nonsmooth optimization is an important branch of optimization theories and methods, various methods for solving these problems have been the key points of optimization theory. At first, the paper simply explicates the bundle method that is an effective method for solving nonsmooth optimization, and elaborate level bundle method which is a kind of classical bundle methods. It constructs the subproblem for generating the next iterative point by using the levels as the constraints. We get the explicit expression of the optimal solution of original subproblem by constructing the Lagrangian function and its dual problem. Finally, we obtain two important conclusions which play an important role in the convergence analysis of the overall algorithm according to the optimality condition and the dual problem of the subproblem.

关 键 词：非光滑优化 束方法 水平束方法 切平面模型 

分 类 号：O221.2[理学—运筹学与控制论]