  This paper proposes and analyzes a tuning-free variant of Primal-Dual Hybrid
Gradient (PDHG), and investigates its effectiveness for solving large-scale
semidefinite programming (SDP). The core idea is based on the combination of
two seemingly unrelated results: (1) the equivalence of PDHG and
Douglas-Rachford splitting (DRS); (2) the asymptotic convergence of
non-stationary DRS. This combination provides a unified approach to analyze the
convergence of generic adaptive PDHG, including the proposed tuning-free
algorithm and various existing ones. Numerical experiments are conducted to
show the performance of our algorithm, highlighting its superior convergence
speed and robustness in the context of SDP.
