基于次梯度选取的非光滑优化强次可行方向法  

Strongly Sub-feasible Direction Method with Subgradient Selection for Nonsmooth Optimization

作　　者：唐春明[1] 简金宝[1] 

机构地区：[1]广西大学数学与信息科学学院,南宁530004

出　　处：《应用数学学报》2011年第5期924-937,共14页Acta Mathematicae Applicatae Sinica

基　　金：国家自然科学基金(71061002);广西自然科学基金(0832052;2010GXNSFB013047);广西教育厅科研基金(20091 1MS202);广西大学科研基金(XBZ100086)资助项目

摘　　要：本文结合次梯度选取技术及割平面法和强次可行方向法的思想,提出了一个求解目标函数非光滑约束优化问题的强次可行方向算法.通过设计一个新的寻找搜索方向子问题和构造新型线搜索,算法不仅能接受不可行的初始点,而且能保持迭代点的强次可行性,同时避免在可行域外目标函数值的不适度增加.算法具备全局收敛性,且初步的数值试验表明算法是稳定有效的.In this paper, by combining subgradient selection technique with the ideas ,of cutting plane method and strongly sub-feasible direction method, a strongly sub-feasible direction algorithm is proposed for the solution of constrained optimization problems with nonsmooth objective function. By introducing a new search direction finding subproblem and constructing a new line search, the algorithm can not only accept infeasible starting points, but also preserve the sub-feasibility of the iterations, and meanwhile prevent the objective value from increasing unduly. The algorithm possesses global convergence, and some preliminary numerical results show that the proposed algorithm is stable and efficient.

关 键 词：次梯度选取 非光滑优化 强次可行方向法 全局收敛 

分 类 号：O221.2[理学—运筹学与控制论]