Research map / Optimization / Nonconvex and smooth optimization
The non-convex Burer-Monteiro approach works on smooth semidefinite programs
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase rank p so that p(p+1)/2 > m (rank-restricted Burer-Monteiro factorization) | Burer-Monteiro SDP surrogate (P) · smooth compact SDPs, almost all cost matrices C | existence of spurious second-order critical points | Helped |
| Use rank p=2 instead of p=3 for Max-Cut BM on cycles where the SDP has a unique rank-1 solution (ablation) | Max-Cut Burer-Monteiro · cycles of certain even lengths | global optimality of local optima | Hurt |
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