ADMM

Under the assumptions of an ideal score and quadratic data fidelity, the authors analyzed the convergence and reconstruction error of the corrected ADMM algorithm.

In the ADMM algorithm, the dual variable u accumulates the constraint violations of successive iterations and feeds them back to the denoiser input, causing a systematic shift between the input distribution the denoiser actually faces and the clean image distribution it was trained on.

The core operation of the S³-PnP framework is to learn a score prior directly on the observation-driven intermediate states of ADMM, requiring neither clean training targets nor external pretrained weights.

In the PnP framework, the z update of ADMM is replaced by one denoiser call, i.e., z^{k+1} = D_σ(x^{k+1} + u^k).

Whether the speedup brought by ADMM can be maintained on larger-scale models (such as the hundred-billion level), and whether influence functions are still preserved under more aggressive compression ratios beyond 2:4 sparsity, are directions not fully covered by the original text.

CACTUS is an optimizer based on ADMM (alternating direction method of multipliers) used to solve the curvature-aware pruning objective, supporting two weight transformation modes: pure pruning and sparse plus low-rank decomposition.

ADMM is an algorithmic framework for solving separable convex optimization problems, proposed by Gabay and Mercier in 1976, whose core idea is to introduce auxiliary variables to decompose the original problem into multiple subproblems, alternately updating the primal variables, auxiliary variables and dual variables.

Previous Gaussian BROJA numerical optimization methods rely on the Alternating Direction Method of Multipliers (ADMM) or similar convex optimization algorithms, requiring dozens to hundreds of iterations per computation.

Representative algorithms of first-order optimization methods include ADMM (Alternating Direction Method of Multipliers) and PDHG (Primal-Dual Hybrid Gradient method).