Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUT
We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape.
ProofPaper ↗
Key points
- Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization.
- 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.
- 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.
- Gains are largest on sparse weighted graphs; on dense graphs we complement the pipeline with spectral sparsification.
Sources (1)
- [1]Graph Coarsening Enables Escaping Local Optima in Compute-Constrained Nonconvex MAX-CUTarXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 13, 06:32 PM
We study Particle Polynomial Relaxation (PPR), a moment-based nonconvex continuous reformulation possessing an advantageous optimization landscape.
Because its binary optimization landscape contains exponentially many local optima, MAX-CUT is highly sensitive to initialization.
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