Compact Lifted Relaxations for Low-Rank Optimization
We develop tractable convex relaxations for rank-constrained quadratic optimization problems over $n \times m$ matrices, a setting for which tractable relaxations are typically only available when the objective or constraints admit spectral structure. We derive lifted semidefinite relaxations that do not require such spectral terms. Although a direct lifting introduces a large semidefinite constraint in dimension $n^2 + nm + 1$, we prove that many blocks of the moment matrix are redundant and derive an equivalent compact relaxation that only involves two semidefinite constraints of dimension $nm + 1$ and $n+m$, respectively. We also derive a new class of valid inequalities for low-rank pr...
| Authors | Ryan Cory-Wright, Jean Pauphilet |
|---|---|
| Primary category | math.OC |
| Published | 5 March 2026 |
| Last updated at source | 20 May 2026 |
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