Transformed primal-dual methods for nonlinear saddle point systems

Abstract A transformed primal-dual (TPD) flow is developed for a class of nonlinear smooth saddle point system. The the dual variable contains Schur complement which strongly convex. Exponential stability obtained by showing strong Lyapunov property. Several TPD iterations are derived implicit Euler, explicit implicit-explicit and Gauss-Seidel methods with accelerated overrelaxation flow. Generalized to symmetric iterations, linear convergence rate preserved convex-concave systems under assumptions that regularized functions effectiveness augmented Lagrangian can be explained as regularization non-strongly convexity preconditioning complement. algorithm analysis depends crucially on appropriate inner products spaces primal variable. clear inexact solvers also developed.