We propose a second order gradient based method with ADAM and RMSprop for the training of generative adversarial networks. The proposed method is fastest to obtain similar accuracy when compared to prominent second order methods. Unlike state-of-the-art recent methods, it does not require solving a linear system, or it does not require additional mixed second derivative terms. We derive the fixed point iteration corresponding to proposed method, and show that the proposed method is convergent. The proposed method produces better or comparable inception scores, and comparable quality of images compared to other recently proposed state-of-the-art second order methods. Compared to first order methods such as ADAM, it produces significantly better inception scores. The proposed method is compared and validated on popular datasets such as FFHQ, LSUN, CIFAR10, MNIST, and Fashion MNIST for image generation tasks\footnote{Accepted in IJCNN 2023}. Codes: \url{https://github.com/misterpawan/acom}

翻译：我们提出了一种基于二阶梯度的方法，结合了ADAM和RMSprop，用于训练生成对抗网络。与著名的二阶方法相比，所提方法在获得类似精度时速度最快。与最新的现有方法不同，它不需要求解线性系统，也不需要额外的混合二阶导数项。我们推导了所提方法对应的不动点迭代，并证明该方法是收敛的。与其他最新提出的二阶方法相比，所提方法产生了更好或可比的初始分数，以及可比的图像质量。与ADAM等一阶方法相比，它产生了显著更好的初始分数。所提方法在FFHQ、LSUN、CIFAR10、MNIST和Fashion MNIST等流行数据集上进行了比较和验证，用于图像生成任务\footnote{已被IJCNN 2023接收}。代码：\url{https://github.com/misterpawan/acom}