一类改进的谱共轭梯度法

An Improved Spectral Conjugate Gradient Method

谱共轭梯度法有两个方向控制参数,是解决大规模无约束优化问题的有效方法.本文提出了一个改进的谱参数θ_k,它不同于现有的θ_k.新算法在任何线搜索下都满足著名的共轭条件:d^T_ky_(k-1)=0.新方法的搜索方向在任何线搜索下都是充分下降的.在一般假设下,我们证明该方法在改进的Wolfe线搜索是全局收敛的.

The spectral conjugate gradient method with two directional control parameters is an effective method for solving large scale unconstrained optimization problems. This paper presents an improved spectral parameter θ k , which is different from the existing one. The new algorithm satisfies the famous conjugate condition: d T ky k-1 =0 , independent of any line search. The search direction of the new method has sufficient descent property under any linear search rules. Under the general assumption, we prove that the new method is globally convergent in the modified Wolfe line search.