Recently, the generalized primal-dual (GPD) method was developed for saddle-point problems (SPPs) with a linear coupling operator. However, the coupling operator in many engineering applications is nonlinear. In this letter, we propose a generalized primal-dual correction method (GPD-CM) to handle SPPs with a nonlinear coupling operator. To achieve this, we customize the proximal matrix and corrective matrix by adjusting the values of regularization factors. By the unified framework, the convergence of GPD-CM is directly obtained. Numerical results on a SPP with an exponential coupling operator support theoretical analysis.

翻译：最近，针对线性耦合算子的鞍点问题（SPPs）发展了广义原始对偶（GPD）方法。然而，许多工程应用中的耦合算子是非线性的。本文提出了一种广义原始对偶校正方法（GPD-CM），用于处理具有非线性耦合算子的SPPs问题。为此，我们通过调整正则化因子的取值来定制近端矩阵和校正矩阵。基于统一框架，GPD-CM的收敛性可直接得到证明。针对具有指数型耦合算子的SPP问题的数值结果验证了理论分析。