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Semidefinite Programming

SIAM Review, 1996
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.
Lieven Vandenberghe, Stephen Boyd
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On the Complexity of Semidefinite Programs

Journal of Global Optimization, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Lorant Porkolab, Leonid Khachiyan
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Conditioning of semidefinite programs

Mathematical Programming, 1999
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Madhu V. Nayakkankuppam   +1 more
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The Simplest Semidefinite Programs are Trivial

Mathematics of Operations Research, 1995
We consider optimization problems of the following type: [Formula: see text] Here, tr(·) denotes the trace operator, C and X are symmetric n × n matrices, B is a symmetric m × m matrix and A(·) denotes a linear operator. Such problems are called semidefinite programs and have recently become the object of considerable interest due to important ...
Robert J. Vanderbei, Bing Yang
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Semidefinite programming

European Journal of Operational Research, 2002
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A Global Algorithm for Nonlinear Semidefinite Programming

open access: yesSIAM Journal on Optimization, 2004
In this paper we propose a global algorithm for solving nonlinear semidefinite programming problems. This algorithm, inspired by the classic SQP (sequentially quadratic programming) method, modifies the S-SDP (sequentially semidefinite programming) local
Rafael Correa, Hector Ramirez C
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The Volumetric Barrier for Semidefinite Programming

Mathematics of Operations Research, 2000
We consider the volumetric barrier for semidefinite programming, or “generalized” volumetric barrier, as introduced by Nesterov and Nemirovskii. We extend several fundamental properties of the volumetric barrier for a polyhedral set to the semidefinite case.
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Semidefinite programming and combinatorial optimization

Mathematical Programming, 1997
We discuss the use of semidefinite programming for combinatorial optimization problems. The main topics covered include (i) the Lovász theta function and its applications to stable sets, perfect graphs, and coding theory, (ii) the automatic generation of strong valid inequalities, (iii) the maximum cut problem and related problems, and (iv) the ...
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