PDHG converges locally linearly for SDP under strict complementarity or primal-dual nondegeneracy, and can converge sublinearly when both fail.
Faster first-order primal-dual methods for linear programming using restarts and sharpness.Mathematical Programming, 201(1–2):133–184, 2023
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Local Linear Convergence of the Primal-Dual Hybrid Gradient Method for Semidefinite Programming
PDHG converges locally linearly for SDP under strict complementarity or primal-dual nondegeneracy, and can converge sublinearly when both fail.