Linear convergence of ADUCA without using the strong convexity parameter in the extrapolation weight

Prove that the Adaptive Delayed-Update Cyclic Algorithm (ADUCA), applied to generalized Minty variational inequalities with a monotone Lipschitz operator and a block-separable strongly convex regularizer g (with modulus μ>0), achieves a linear convergence rate even when the algorithm sets μ=0 in the extrapolation weight ω_k = (1 + ρβ μ a_k) / (1 + μ a_k), i.e., when ω_k ≡ 1 and no knowledge of μ is used in the updates.

Background

ADUCA attains near-linear convergence under strong convexity by using the parameter μ in the sequence of extrapolation weights ω_k = (1 + ρβ μ a_k) / (1 + μ a_k). In practice, μ may be unknown; the paper shows that replacing μ with any conservative lower bound preserves theoretical guarantees and that empirical performance is largely insensitive to the choice of μ.

Motivated by ablation experiments in which setting μ = 0 (hence ω_k ≡ 1) led to convergence behavior indistinguishable from runs with higher μ, the authors conjecture that ADUCA can be proven to converge linearly even when μ is not used in ω_k. Establishing such a result would remove the need for μ in the algorithm’s extrapolation step while retaining linear rates under strong convexity, but the authors note that proving this likely requires a more complex analysis.