aiqbench analysis
This research proposes a novel optimization pipeline combining spectral graph coarsening with particle polynomial relaxation to solve the nonconvex MAX-CUT problem more efficiently. By leveraging structure-aware initialization without training data, the method significantly reduces memory requirements and escapes local optima on large-scale sparse graphs. The approach represents a meaningful advancement in algorithmic efficiency for combinatorial optimization tasks within constrained compute environments.
Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT
arXiv:2610.19043v1 Announce Type: cross Abstract: Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization. We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape. We warm-start PPR with Combinatorial Multigrid (CMG), a spectral graph-coarsening method that produces structure-aware initial solutions in near-linear time without training data. On \texttt{t2g20} ($n=400$), benchmark instance with known exact optimum, the combined CMG+PPR pipeline reaches $97.5\%$ of optimum on average and $98.4\%$ on the best run. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method. Using a sparse CSR representation, the same approach scales to G-set instances with up to $20{,}000$ vertices reducing memory requirements by up to $3333\times$ while maintaining a consistent improvement over the CMG warm start. Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.
Abstract:Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization. We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape. We warm-start PPR with Combinatorial Multigrid (CMG), a spectral graph-coarsening method that produces structure-aware initial solutions in near-linear time without training data. On \texttt{t2g20} ($n=400$), benchmark instance with known exact optimum, the combined CMG+PPR pipeline reaches $97.5\%$ of optimum on average and $98.4\%$ on the best run. An extended variant with discrete local-search refinement reaches the published optimum on all sixty Biq Mac instances evaluated by a recent neural branch-and-bound method. Using a sparse CSR representation, the same approach scales to G-set instances with up to $20{,}000$ vertices reducing memory requirements by up to $3333\times$ while maintaining a consistent improvement over the CMG warm start. Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.
Machine Learning (cs.LG); Artificial Intelligence (cs.AI); Computation and Language (cs.CL); Numerical Analysis (math.NA); Optimization and Control (math.OC)
arXiv:2610.19043 [cs.LG]
(or arXiv:2610.19043v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2610.19043 arXiv-issued DOI via DataCite (pending registration)
From: M. Harper Langston [view email] [v1] Tue, 13 Oct 2026 18:32:31 UTC (1,689 KB)
Full text under the publisher's open licence · 201 words
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