A Symmetry-Preserving Extrapolated Primal-Dual Hybrid Gradient Method for Saddle-Point Problems

The primal-dual hybrid gradient (PDHG) method is widely used for convex–concave saddle-point problems, yet its extrapolated variants are typically asymmetric because only one side is extrapolated. We propose a symmetry-preserving refinement, E-PDHG, which performs dual-side extrapolation followed by an explicit correction step. Under standard step-size conditions, we establish global convergence for all η∈(−1,1) and derive a pointwise (non-ergodic) O(1/t) rate for the last iterate. The method does not improve the asymptotic complexity order of PDHG; instead, it enlarges the practically stable parameter region while retaining the same per-iteration cost. Numerical experiments on image deblurring/inpainting and additional machine learning benchmarks (logistic regression and LASSO) demonstrate improved finite-iteration stability and efficiency.