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Zbl 0845.65023
Vandenberghe, Lieven; Boyd, Stephen
Semidefinite programming. (English)
[J] SIAM Rev. 38, No. 1, 49-95 (1996). ISSN 0036-1445; ISSN 1095-7200/e

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 quadratic programming) and finds many applications in engineering and combinatorial optimization.\par Although semidefinite programs are much more general than linear programs, they are not much harder to solve. This paper gives a survey of the theory and applications of semidefinite programs and an introduction to primal-dual interior-point methods for their solution.
[N.Djuranović-Miličić (Beograd)]

MSC 2000:: *90C22 Semidefinite programming
90C51 Interior-point methods
90-02 Research monographs (optimization)
65K05 Mathematical programming (numerical methods)
90C27 Combinatorial programming
90C25 Convex programming

Keywords: survey article; semidefinite programming; convex optimization; combinatorial optimization; primal-dual interior-point methods

Cited in: Zbl 1176.14010 Zbl 1153.90522

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