基于非单调线搜索的对角二阶拟牛顿法  

A Diagonal Second-order Quasi-newton Method Based on the Non-monotone Line Search Rule

作　　者：朱帅[1] 鲍莹莹[2] 王希云[2] 

机构地区：[1]山西大同大学工学院,山西大同037003 [2]山西太原科技大学应用科学学院,山西太原030024

出　　处：《数学的实践与认识》2014年第6期226-232,共7页Mathematics in Practice and Theory

摘　　要：在二阶拟牛顿方程的基础上,结合Zhang H.C.提出的非单调线搜索构造了一种求解大规模无约束优化问题的对角二阶拟牛顿算法.算法在每次迭代中利用对角矩阵逼近Hessian矩阵的逆,使计算搜索方向的存储量和工作量明显减少,为大型无约束优化问题的求解提供了新的思路.在通常的假设条件下,证明了算法的全局收敛性和超线性收敛性.数值实验表明算法是有效可行的.Based on the second order Quasi-Newton equation, and combined with the non- monotone line search rule which was proposed by Zhang H C, we propose a diagonal second order Quasi-Newton method for large-scale unconstrained optimization problems. The algo- rithm uses a diagonal matrix approximation of the inverse Hessian matrix at each iteration, which significantly reduces the storage capacity and workload of computing the search direc- tion and provides a new way of thinking to solve the large-scale unconstrained optimization problem. Under the usual assumptions, the method proves the global convergence and super- linear convergence. Numerical experiments show that the algorithm is effective and feasible.

关 键 词：关键词 无约束优化问题 二阶拟牛顿方程 非单调线搜索 局收敛性 超线性收敛性 

分 类 号：O224[理学—运筹学与控制论]