求不定二次规划全局最优解的新的线性化技术  

A New linear Relaxed Technology for Solving Global Optimal Solution of Indefinite Quadratic Programming

作　　者：蔡剑[1] 

机构地区：[1]南京航空航天大学金城学院,南京211156

出　　处：《西安文理学院学报（自然科学版）》2015年第3期1-4,共4页Journal of Xi’an University(Natural Science Edition)

基　　金：国家自然科学基金青年基金资助项目(11101213)

摘　　要：为了提高非线性约束的不定二次规划求解速度,提出了一种松弛线性规划的新算法.首先利用不定二次函数自身的特点,将其转化为凸二次函数;其次利用凸函数可以找到线性下界的特点,采用线性化技术建立不定二次规划的松弛线性规划;最后利用分支定界算法,通过对可行域的细分,缩小求解范围,最终求得最优值点.开展了实例计算,计算结果显示松弛线性规划算法能显著提升不定二次规划求全局最优解的速度.In order to improve the solving speed of indefinite quadratic programming,a new relaxed linear programming algorithm was provided. Firstly,the function was turned into a convex quadratic function with its characteristics. Secondly,with the characteristics of the convex function has its linear lower bound,relaxed linear programming function was established by using of the linearization technology. Finally,by using of the branch and bound algorithm,the solving range was narrowed and the feasible region was subdivided,eventually the optimal value was obtained. Examples of calculation were carried out,and the calculation results show that the new algorithm of relaxed linear programming can significantly improve the solving speed of indefinite quadratic programming.

关 键 词：不定二次规划 线性化技术 松弛线性规划 全局最优解 

分 类 号：O221.2[理学—运筹学与控制论]