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Semidefinite Programming
Abstract
In semidefinite programming, one minimizes a linear function subject to the constraint that an affine combination of symmetric matrices is positive semidefinite. Such a constraint is nonlinear and nonsmooth, but convex, so semidefinite programs are convex optimization problems. semidefinite programming unifies several standard problems (e.g., linear and quadratic programming) and finds many applications in engineering and combinatorial optimization. Although semidefinite programs are much more general than linear programs, they are not much harder to solve. Most interior-point methods for linear programming have been generalized to semidefinite programs. As in linear programming, these methods have polynomial worst-case complexity and perform very well in practice. This paper gives a survey of the theory and applications of semidefinite programs and an introduction to primaldual interior-point methods for their solution.
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Cited by
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Exact Matrix Completion via Convex Optimization
Candès, E. J., & Recht, B. (2009) · Foundations of Computational Mathematics · doi:10.1007/s10208-009-9045-5 · Cited by 4,877
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Luo, Z.-Q., Ma, W.-K., So, A., Ye, Y., & Zhang, S. (2010) · IEEE Signal Processing Magazine · doi:10.1109/msp.2010.936019 · Cited by 3,715
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
Gühne, O., & Tóth, G. (2009) · Physics Reports · doi:10.1016/j.physrep.2009.02.004 · Cited by 2,401
Metadata
- Authors
- Vandenberghe, L., & Boyd, S.
- Venue
- SIAM Review
- Published
- 1996-03
- Volume
- 38
- Issue
- 1
- Pages
- 49-95
- ISSN
- 0036-1445 (ISSN-L)
- 1095-7200
- OpenAlex
- W2912522929
- Cited by
- 4,105
- References
- 0
- FWCI
- 80.65
- Type
- journal article
- Language
- en
- Open access
- closed
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