Automating Reformulation for Parallel ADMM

TL;DR

This paper introduces an automated pipeline that reformulates complex multiblock optimization problems into a two-block structure, enhancing the efficiency of parallel ADMM algorithms through graph-based techniques and machine learning guidance.

Contribution

It presents a novel, fully automated method for converting multiblock problems into ADMM-compatible forms using graph transformations, MILP, and GNN models, implemented in Julia.

Findings

Reformulations improve parallel ADMM performance.

Graph-based edge subdivision effectively decomposes problems.

The pipeline is available as an open-source Julia package.

Abstract

Many real-world optimization models contain exploitable sparsity and block structure, but this structure is often obscured in algebraic form, limiting the effectiveness of modern parallel algorithms. We propose an automatic pipeline that converts a generic multiblock problem into a canonical two-block formulation suitable for parallel Alternating Direction Method of Multipliers (ADMM). The method constructs a coupling graph, applies an edge-subdivision-based bipartization to obtain a bipartite representation, and produces an ADMM-ready decomposition with independent subproblems. Fast graph-traversal heuristics, a new mixed-integer linear program (MILP), and a learning-based graph neural network (GNN) surrogate model are developed to guide edge subdivision. Numerical experiments demonstrate that the resulting reformulations yield strong parallel ADMM performance. The entire pipeline is implemented in the open-source Julia package PDMO.jl.