基于松弛策略解半无限规划模型的显式修正算法  

A Modified Explicit Algorithm Based-Relaxation-Strategy for Solving Semi-infinite Programming

作　　者：杜廷松[1] 杨静俐[1] 沈艳军[1] 费浦生[2] 

机构地区：[1]三峡大学理学院,湖北宜昌443002 [2]武汉大学数学与统计学院,湖北武汉430072

出　　处：《数学的实践与认识》2011年第9期154-161,共8页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10726016);湖北省教育厅优秀中青年科技创新团队项目(T200809);湖北省自然科学基金(2008CDZ046)

摘　　要：讨论了一类线性半无限最优规划模型的求解算法.采用松弛方法解其系列子问题LP(T_k)及DLP(T_k),基于松弛策略和在适当的假设条件下,提出了一个我们称之为显式算法的新型算法.新算法的主要改进之处是算法在每一步迭代计算时,允许丢弃一些不必要的约束.在这种方式下,算法避免了求解系列太大规模的子问题.最后,基于提出的显式修正算法,并与传统割平面方法和已有文献中的松弛修正算法、对同一问题作了初步的数值比较实验.In this paper, we investigate a class of linear semi-infinite programming. We adopt the relaxation-approach such that a sequence of linear programsLP（Tk） and DLP（Tk） is solved. Based on the relaxed strategies, and under some conditions, a new explicit algorithm is developed. The major improvement of the proposed new algorithm is that it allows the unnecessary constraints to be dropped at each iteration. In this way, the proposed algorithm avoid solving too large problems. Finally, three different algorithms （namely, the proposed explicit algorithm, the traditional cutting plane method, and the modification algorithm published literature） have been implemented for same problems.

关 键 词：半无限规划 显式算法 松弛策略 

分 类 号：O221[理学—运筹学与控制论]