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@@ -139,7 +139,7 @@ Under the negative comonotonicity with $\begin{array} { r } { - \frac { 1 } { 8
 
 # 4.2 Comparison to EAG under the monotonicity $( \rho = 0$ )
 
-For an $L$ -Lipschitz continuous and monotone operator $\pmb { F }$ , [43] proposed two EAG methods, named EAG-C and EAG-V, with same βk = 1k+2 but with different choices of $\alpha _ { k }$ . EAG-C sets $\alpha _ { k }$ to be a constant $\frac { 1 } { 8 L }$ for all $k \geq 0$ in (EAG), and has a large constant 260 in its convergence rate, $\begin{array} { r } { \| \pmb { F } \pmb { z } _ { k } \| ^ { 2 } \le \frac { 2 6 0 L ^ { 2 } \| \pmb { z } _ { 0 } - \pmb { z } _ { * } \| ^ { 2 } } { ( k + 1 ) ^ { 2 } } } \end{array}$ 260L2kz0−z∗k22 for all k ≥ 0. On the other hand, while EAG-V requires a complicated recursive update for {αk}, αk+1 = αk1−α2L2  $\begin{array} { r } { \alpha _ { k + 1 } = \frac { \alpha _ { k } } { 1 - \alpha _ { k } ^ { 2 } L ^ { 2 } } \big ( 1 - \frac { ( k + 2 ) ^ { 2 } } { ( k + 1 ) ( k + 3 ) } \alpha _ { k } ^ { 2 } L ^ { 2 } \big ) } \end{array}$ for all $k \geq 0$ , with $\begin{array} { r } { \alpha _ { 0 } = \frac { 0 . 6 1 8 } { L } } \end{array}$ , its rate has a smaller constant 27.
+For an $L$ -Lipschitz continuous and monotone operator $\pmb { F }$ , [43] proposed two EAG methods, named EAG-C and EAG-V, with same βk = 1k+2 but with different choices of $\alpha _ { k }$ . EAG-C sets $\alpha _ { k }$ to be a constant $\frac { 1 } { 8 L }$ for all $k \geq 0$ in (EAG), and has a large constant 260 in its convergence rate, $\begin{array} { r } { \| \pmb { F } \pmb { z } _ { k } \| ^ { 2 } \le \frac { 2 6 0 L ^ { 2 } \| \pmb { z } _ { 0 } - \pmb { z } _ { * } \| ^ { 2 } } { ( k + 1 ) ^ { 2 } } } \end{array}$ 260L2kz0−z∗k22 for all k ≥ 0. On the other hand, while EAG-V requires a complicated recursive update for {αk}, αk+1 = αk1−α2L2  $\begin{array} { r } { \alpha _ { k + 1 } = \frac { \alpha _ { k } } { 1 - \alpha _ { k } ^ { 2 } L ^ { 2 } } \big ( 1 - \frac { ( k + 2 ) ^ { 2 } } { ( k + 1 ) ( k + 3 ) } \alpha _ { k } ^ { 2 } L ^ { 2 } \big ) } \end{array}$ for all $k \geq 0$ , with $\begin{array} { r } { \alpha _ { 0 } = \frac { 0 . 6 1 8 } { L } } \end{array}$ , its rate has a smaller constant 27.
 
 ![](images/380353bbf2580099fbe770143af658fb4debcb8120afd75852aaa71dc5266deb.jpg)  
 Figure 2: Numerical result with $\begin{array} { r } { f ( x , y ) = - \frac { 1 } { 6 } x ^ { 2 } + \frac { 2 \sqrt { 2 } } { 3 } x y + \frac { 1 } { 6 } y ^ { 2 } } \end{array}$ . The dashed line represents the theoretical bound (3) of FEG.