  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.
