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• W2426334170 abstract "Semidefinite programs (SDPs) can be solved in polynomial time by interior point methods, but scalability can be an issue. To address this shortcoming, over a decade ago, Burer and Monteiro proposed to solve SDPs with few equality constraints via rank-restricted, non-convex surrogates. Remarkably, for some applications, local optimization methods seem to converge to global optima of these non-convex surrogates reliably. Although some theory supports this empirical success, a complete explanation of it remains an open question. In this paper, we consider a class of SDPs which includes applications such as max-cut, community detection in the stochastic block model, robust PCA, phase retrieval and synchronization of rotations. We show that the low-rank Burer--Monteiro formulation of SDPs in that class almost never has any spurious local optima." @default.
• W2426334170 created "2016-06-24" @default.
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• W2426334170 date "2016-06-15" @default.
• W2426334170 modified "2023-09-27" @default.
• W2426334170 title "The non-convex Burer-Monteiro approach works on smooth semidefinite programs" @default.
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