求解无约束优化问题的一类谱共轭梯度法

A class of spectral conjugate gradient methods for unconstrained optimization problem

针对无约束优化问题,提出一类谱共轭梯度法.谱共轭梯度法是对TS、GN及MPRP方法的修正,使得在任何线性搜索条件下都具有充分下降性.并且在Armijo型线性搜索条件下,证明了该类算法的全局收敛性.与GN、SFR及MPRP方法进行比较,数值结果表明:谱共轭梯度法是可行的,特别对于大规模无约束优化问题更有效.

A class of spectral conjugate gradient algorithms were presented for solving unconstrained optimization problems. These methods are the modifications of the TS, GN and MPRP methods, which possess sufficient descent property under any linear search rules. The global convergence of the given methods can be established under Armijo-type line search condition. By comparing these methods with the GN, SFR and PRP methods, the numerical results show that these methods are feasible, and more effective for the large scale unconstrained optimization problems.