解非凸二次规划的分支定界缩减方法  

An efficient branch-and-bound reduced algorithm for solving a class of non-convex quadratic programming

作　　者：井霞 高磊 

机构地区：[1]宝鸡文理学院数学与信息科学学院,陕西宝鸡721013

出　　处：《宝鸡文理学院学报（自然科学版）》2017年第4期5-9,15,共6页Journal of Baoji University of Arts and Sciences(Natural Science Edition)

基　　金：陕西省自然科学基础研究项目(2017JQ3020);陕西省高校科协青年人才托举项目资助(20160234);宝鸡文理学院校级科研项目(ZK2017095;ZK2017021)

摘　　要：目的研究带有二次约束的非凸二次规划问题。方法采用二级松弛技术、超矩形缩减与剪支技术。结果与结论提出了确定该类问题全局最优值的分支定界缩减算法,并证明了算法是收敛的,并用数值算例验证了算法的可行性与有效性。Purpose-To study a class of non-convex quadratic programming problem with quadrat- ic constraints. Methods-Two-level relaxation technique and a rectangular reduction-cut strategy are used to solve the aforesaid problem. Conclusion and Results-The convergence of the new algorithm is proved in addition to presenting a new braneh-and-bound reduced algorithm for determining the global optimal value. The feasibility and effectiveness of this algorithm are verified by numerical examples.

关 键 词：全局最优值 二次约束 非凸二次规划 分支定界 

分 类 号：O221.2[理学—运筹学与控制论]