Alternating Direction Method of Multipliers

Also known as ADMM

ADMM studies how to solve constrained optimization problems by splitting them into simpler subproblems and coordinating their solutions with dual-variable updates. Consensus, proximal, linearized, and multi-block variants are used in distributed learning, inverse problems, model-predictive control, robotics, and compression; common evaluations include image reconstruction, quadratic-program benchmarks, and trajectory-planning tasks. Current work combines ADMM with GPU implementations, learned parameter updates, and deep unfolding, while plug-and-play variants incorporate denoisers or generative priors. A central tension is how to gain speed and flexibility without losing convergence and constraint guarantees, particularly for nonconvex or multi-block problems where convergence can fail.

Latest papers

32 papers2 papers in the last four weeks, against 2 the four weeks before. 0.0% of all new papers.

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming
Jun 2, 2025Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka +1Graph Structure Learning Graph Representation Learning
On the Relationship Between CoCoA and ADMM for Distributed Empirical Risk Minimization
Feb 1, 2025Runxiong Wu, Andi WangPrimal-Dual Optimization Distributed Optimization
Department of Industrial & Systems Engineering University of Wisconsin–Madison

Jun 2, 2025J/K move · Enter open · S save

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

Haruki Yokota, Hiroshi Higashi, Yuichi Tanaka, Gene Cheung

Graph Structure Learning Graph Representation Learning Alternating Direction Method of Multipliers Linear Programming

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Signed graphs are equipped with both positive and negative edge weights, encoding pairwise correlations as well as anti-correlations in data. A balanced signed graph is a signed graph with no cycles containing an odd number of negative edges. Laplacian of a balanced signed graph has eigenvectors that map via a simple linear transform to ones in a corresponding positive graph Laplacian, thus enabling reuse of spectral filtering tools designed for positive graphs. We propose an efficient computation method to learn a balanced signed graph Laplacian directly from data. Specifically, extending a previous linear programming (LP) based sparse inverse covariance estimation method called CLIME, we formulate a new LP problem for each Laplacian column

i

, where the linear constraints restrict weight signs of edges stemming from node

i

, so that nodes of same / different polarities are connected by positive / negative edges. We derive a feasible CLIME parameter

ρ_i

for each sign-constrained column problem. We solve the LP problem efficiently by tailoring a sparse LP method based on ADMM. We theoretically prove that the row / column updates produce a non-increasing objective sequence, and show that the iterations are terminated in a finite number of steps. Extensive experimental results on synthetic and real-world datasets show that our balanced graph learning method outperforms competing methods and enables reuse of spectral filters, wavelets, and graph neural nets (GNN) constructed for positive graphs.

Latest papers

Efficient Learning of Balanced Signed Graphs via Sparse Linear Programming

On the Relationship Between CoCoA and ADMM for Distributed Empirical Risk Minimization