We propose an effective GPU-accelerated alternating direction method of multipliers (ADMM) solver tailored for solving large-scale problems of lower-bound (LB) finite element limit analysis (FELA), formulated as sparse second-order cone programs (SOCPs). For the past two decades, Interior-Point Methods (IPMs) have been the dominant optimization technique of choice for FELA problems. However, the IPM can suffer from scalability issues because it needs to reform and refactorize the Karush Kuhn-Tucker (KKT) matrix in every iteration. Although the development of domain-specific, high-performance IPM solvers—exploiting problem structure and GPU parallelism—has alleviated some of these challenges, and such bespoke solvers may outperform commercial IPM solvers [1], the fundamental limitations of IPMs remain significant for large-scale applications. Recent advances have seen the application of ADMM, a first-order optimization method, in the context of FELA [2], demonstrating its potential as a robust solver capable of handling large-scale 2D and 3D limit analysis problems. ADMM benefits from cheaper per-iteration computational cost and relatively low memory requirements [3]. ADMM is guaranteed to converge for convex problems, but it can be slow to converge to high accuracy [4]. To improve the performance of ADMM for SOCP problems of the type that arise in FELA, we periodically identify the active SOC constraints and adaptively modify the corresponding penalty parameters in the augmented Lagrangian [5], which substantially reduces the number of iterations while preserving robustness. In addition, we exploit the warm-starting capability of ADMM to speed up convergence when performing a sequence of adaptive mesh refinements for a given problem. The dominant sparse linear solves and matrix-vector operations are executed entirely on the GPU using CUDA. Comparison of the proposed ADMM solver with various IPM solvers has demonstrated its efficiency and robustness on large-scale FELA benchmarks with up to 6 million variables.