非凸二次规划问题的一个全局优化方法  

A Global Optimization Methods for Non-convex Quadratic Programming

作　　者：王杉林[1] 

机构地区：[1]兰州商学院陇桥学院,兰州730101

出　　处：《重庆师范大学学报（自然科学版）》2015年第3期17-22,共6页Journal of Chongqing Normal University:Natural Science

摘　　要：考虑的问题是线性约束下极小化二次目标函数的数学规划问题(QP)。在可行域是非空紧集假设下,利用KKT条件,将原问题等价转化为带线性互补约束、线性目标函数的问题(LPC),对(LPC)提出了一个全局优化算法。该方法的主要思想是生成一个点对序列,使它或在有限步迭代后终止于(LPC)的最优解或收敛于(LPC)的最优解。证明了算法的收敛性,并通过求解构造的实例说明了此方法的有效性。Considering the problem QP is that minimum quadratic objective function with linear constraints. Under the hypothesis of the feasible region is non-empty compact set, using the KKT conditions of the problem, to bring the original problem is transformed into the problem of linear objective function with complementarity＇s constraints LPC. On a global optimization algorithm is pro- posed. The main idea of the method is to generate a sequence of points either ending at a global optimal solution within a finite num- ber of iterations or converging to a global optimal solution of the LPC. To prove the finite convergence of the algorithm and by sol- ving construction example is given to illustrate the effectiveness of this method.

关 键 词：非凸二次规划 全局优化 线性互补问题 最优解 收敛性 

分 类 号：O221.2[理学—运筹学与控制论]