能克服鞍点的并行计算寻优算法  

Parallel computing optimization algorithm for overcoming the saddle point

作　　者：李炯城[1] 肖恒辉[1] 李桂愉[1] 

机构地区：[1]广东省电信规划设计院有限公司广州市无线网络优化重点工程中心,广东广州510630

出　　处：《计算机工程与设计》2012年第12期4589-4593,共5页Computer Engineering and Design

基　　金：广东省教育部产学研结合基金项目(2009B090300393);广州市软件(动漫)产业发展基金项目(2060404)

摘　　要：为有效解决在求解具有鞍点的无约束最优化问题时寻优算法提前终止的问题,提出了一种能克服鞍点的计算机并行计算寻优算法。该算法以共轭梯度法为基础,对该算法寻优终止的条件进一步改进,提出当算法迭代到鞍点时,选择雅克比矩阵的所有正特征值对应的特征向量所对应的方向作为新的搜寻方向,重新搜索且并行计算取最优。最后通过实例验证了该算法能成功克服鞍点,并成功收敛到函数的极小值。To solve the problem that the optimization algorithm is terminated ahead of time when solving the unstrained planning problem with saddle points effectively, a parallel computing optimization algorithm is proposed, which can overcome the saddle point. This algorithm is based on conjugate gradient method, and the condition of algorithm termination is improved further. When it terminates to saddle points, this optimization algorithm will choose the directions which are all eigenvectors for all the positive eigenvalue of Jacobi matrix, then continue to parallel computing and choose the optimal solution at last. Finally, the al- gorithm is proved by an example that it can overcome saddle point successfully, and be iteration to the minimum of function suc- cessfully.

关 键 词：寻优算法 鞍点 共轭梯度法 海赛矩阵 雅克比矩阵 

分 类 号：TP183[自动化与计算机技术—控制理论与控制工程]