算法3 非单调Wolfe线搜索

输入： $m_0$ , $j=0$ , ${\alpha }_{\min }=0$ , ${\alpha }_{\max }=0$ , $Q_0=1$ , $C_0=f\left(m_0\right)$ , $0\le {\eta }_{\min }\le {\eta }_{\max }\le 1$ , $0<{\sigma }_1<{\sigma }_2<1$

初始化： ${\alpha }_j=1$

while true

1：if ${\alpha }_j$ 满足(6)和(7)计算 $f\left(m_k+{\alpha }_j\delta m\right)$ end

2：if ${\alpha }_j$ 不满足(6) ${\alpha }_{\max }={\alpha }_j$ , ${\alpha }_j=\frac{1}{2}\left({\alpha }_{\min }+{\alpha }_{\max }\right)$ 返回步1 end

3：if ${\alpha }_j$ 不满足(7) ${\alpha }_{\min }={\alpha }_j$

if ${\alpha }_{\max }=0$ , ${\alpha }_j=10{\alpha }_j$ else ${\alpha }_j=\frac{1}{2}\left({\alpha }_{\min }+{\alpha }_{\max }\right)$ end返回步1

end

4：if ${\eta }_j\in \left[{\eta }_{\min },{\eta }_{\max }\right]$ 满足(8)更新 $Q_j,C_j$ end

5： $j\leftarrow j+1$

end while