Matches in SemOpenAlex for { <https://semopenalex.org/work/W4297804089> ?p ?o ?g. }
Showing items 1 to 85 of
85
with 100 items per page.
- W4297804089 abstract "We consider semidefinite programs (SDPs) of size n with equality constraints. In order to overcome scalability issues, Burer and Monteiro proposed a factorized approach based on optimizing over a matrix Y of size $n$ by $k$ such that $X = YY^*$ is the SDP variable. The advantages of such formulation are twofold: the dimension of the optimization variable is reduced and positive semidefiniteness is naturally enforced. However, the problem in Y is non-convex. In prior work, it has been shown that, when the constraints on the factorized variable regularly define a smooth manifold, provided k is large enough, for almost all cost matrices, all second-order stationary points (SOSPs) are optimal. Importantly, in practice, one can only compute points which approximately satisfy necessary optimality conditions, leading to the question: are such points also approximately optimal? To this end, and under similar assumptions, we use smoothed analysis to show that approximate SOSPs for a randomly perturbed objective function are approximate global optima, with k scaling like the square root of the number of constraints (up to log factors). Moreover, we bound the optimality gap at the approximate solution of the perturbed problem with respect to the original problem. We particularize our results to an SDP relaxation of phase retrieval." @default.
- W4297804089 created "2022-10-01" @default.
- W4297804089 creator A5048166612 @default.
- W4297804089 creator A5067415832 @default.
- W4297804089 creator A5085231507 @default.
- W4297804089 date "2018-06-10" @default.
- W4297804089 modified "2023-09-24" @default.
- W4297804089 title "Smoothed analysis of the low-rank approach for smooth semidefinite programs" @default.
- W4297804089 doi "https://doi.org/10.48550/arxiv.1806.03763" @default.
- W4297804089 hasPublicationYear "2018" @default.
- W4297804089 type Work @default.
- W4297804089 citedByCount "0" @default.
- W4297804089 crossrefType "posted-content" @default.
- W4297804089 hasAuthorship W4297804089A5048166612 @default.
- W4297804089 hasAuthorship W4297804089A5067415832 @default.
- W4297804089 hasAuthorship W4297804089A5085231507 @default.
- W4297804089 hasBestOaLocation W42978040891 @default.
- W4297804089 hasConcept C101901036 @default.
- W4297804089 hasConcept C106487976 @default.
- W4297804089 hasConcept C112680207 @default.
- W4297804089 hasConcept C114614502 @default.
- W4297804089 hasConcept C121332964 @default.
- W4297804089 hasConcept C126255220 @default.
- W4297804089 hasConcept C134306372 @default.
- W4297804089 hasConcept C14036430 @default.
- W4297804089 hasConcept C15744967 @default.
- W4297804089 hasConcept C158693339 @default.
- W4297804089 hasConcept C159985019 @default.
- W4297804089 hasConcept C164226766 @default.
- W4297804089 hasConcept C182365436 @default.
- W4297804089 hasConcept C189237950 @default.
- W4297804089 hasConcept C192562407 @default.
- W4297804089 hasConcept C2524010 @default.
- W4297804089 hasConcept C2776029896 @default.
- W4297804089 hasConcept C28826006 @default.
- W4297804089 hasConcept C33676613 @default.
- W4297804089 hasConcept C33923547 @default.
- W4297804089 hasConcept C49712288 @default.
- W4297804089 hasConcept C62520636 @default.
- W4297804089 hasConcept C77805123 @default.
- W4297804089 hasConcept C78458016 @default.
- W4297804089 hasConcept C86803240 @default.
- W4297804089 hasConcept C99844830 @default.
- W4297804089 hasConceptScore W4297804089C101901036 @default.
- W4297804089 hasConceptScore W4297804089C106487976 @default.
- W4297804089 hasConceptScore W4297804089C112680207 @default.
- W4297804089 hasConceptScore W4297804089C114614502 @default.
- W4297804089 hasConceptScore W4297804089C121332964 @default.
- W4297804089 hasConceptScore W4297804089C126255220 @default.
- W4297804089 hasConceptScore W4297804089C134306372 @default.
- W4297804089 hasConceptScore W4297804089C14036430 @default.
- W4297804089 hasConceptScore W4297804089C15744967 @default.
- W4297804089 hasConceptScore W4297804089C158693339 @default.
- W4297804089 hasConceptScore W4297804089C159985019 @default.
- W4297804089 hasConceptScore W4297804089C164226766 @default.
- W4297804089 hasConceptScore W4297804089C182365436 @default.
- W4297804089 hasConceptScore W4297804089C189237950 @default.
- W4297804089 hasConceptScore W4297804089C192562407 @default.
- W4297804089 hasConceptScore W4297804089C2524010 @default.
- W4297804089 hasConceptScore W4297804089C2776029896 @default.
- W4297804089 hasConceptScore W4297804089C28826006 @default.
- W4297804089 hasConceptScore W4297804089C33676613 @default.
- W4297804089 hasConceptScore W4297804089C33923547 @default.
- W4297804089 hasConceptScore W4297804089C49712288 @default.
- W4297804089 hasConceptScore W4297804089C62520636 @default.
- W4297804089 hasConceptScore W4297804089C77805123 @default.
- W4297804089 hasConceptScore W4297804089C78458016 @default.
- W4297804089 hasConceptScore W4297804089C86803240 @default.
- W4297804089 hasConceptScore W4297804089C99844830 @default.
- W4297804089 hasLocation W42978040891 @default.
- W4297804089 hasOpenAccess W4297804089 @default.
- W4297804089 hasPrimaryLocation W42978040891 @default.
- W4297804089 hasRelatedWork W1409680301 @default.
- W4297804089 hasRelatedWork W1712235185 @default.
- W4297804089 hasRelatedWork W2171800673 @default.
- W4297804089 hasRelatedWork W2747249330 @default.
- W4297804089 hasRelatedWork W2785900686 @default.
- W4297804089 hasRelatedWork W2893860505 @default.
- W4297804089 hasRelatedWork W2950697756 @default.
- W4297804089 hasRelatedWork W2963842491 @default.
- W4297804089 hasRelatedWork W4289490443 @default.
- W4297804089 hasRelatedWork W4301799555 @default.
- W4297804089 isParatext "false" @default.
- W4297804089 isRetracted "false" @default.
- W4297804089 workType "article" @default.