Sublinear time algorithms for approximate semidefinite programming

We consider semidefinite optimization in a saddle point formulation where the primal solution is in the spectrahedron and the dual solution is a distribution over affine functions. We present an approximation algorithm for this problem that runs in sublinear time in the size of the data. To the best...

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Vydáno v:Mathematical programming Ročník 158; číslo 1-2; s. 329 - 361
Hlavní autoři: Garber, Dan, Hazan, Elad
Médium: Journal Article
Jazyk:angličtina
Vydáno: Berlin/Heidelberg Springer Berlin Heidelberg 01.07.2016
Springer Nature B.V
Témata:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Machine learning
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematical models
Mathematical programming
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Optimization
Studies
Theoretical
Large scale optimization
68W20
Online algorithms
Semidefinite programming
90C22
90C06
68W27
Sublinear algorithms
ISSN:0025-5610, 1436-4646
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Popis
Shrnutí:We consider semidefinite optimization in a saddle point formulation where the primal solution is in the spectrahedron and the dual solution is a distribution over affine functions. We present an approximation algorithm for this problem that runs in sublinear time in the size of the data. To the best of our knowledge, this is the first algorithm to achieve this. Our algorithm is also guaranteed to produce low-rank solutions. We further prove lower bounds on the running time of any algorithm for this problem, showing that certain terms in the running time of our algorithm cannot be further improved. Finally, we consider a non-affine version of the saddle point problem and give an algorithm that under certain assumptions runs in sublinear time.
Bibliografie:SourceType-Scholarly Journals-1
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-015-0932-z