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Abstract: . Consider the diagonal entries d j , j = 1, 2, . . . , n, of the matrix D in an LDL T factorization of an n n matrix X . As a function of X , each d j is well-defined on the closed domain of positive semidefinite matrices. We show that these functions are twice continuously differentiable and concave throughout the interior of this domain. Using these facts, we show how to formulate semidefinite programming problems as standard convex optimization problems that can be solved using an... (Update)
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.... 11, 12] who formulate (SDP ) as nonconvex programming problems using low rank factorizations of the primal matrix X, and Vanderbei et al. [43]. Finally we must mention that Burer et al. [13, 14] have come up with attractive heuristics for max cut and maximum stable set problems,...
...exploit the bound on the rank of optimal matrix X in ensuring that X = V V T , where V is a n r matrix for some small r. Vanderbei et al. [43] factor the primal matrix X as LDiag(d)L T , where L is unit triangular and d # IR n . The constraint that X # 0 is replaced with the...
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BibTeX entry: (Update)
R. J. Vanderbei and H. Yurttan Benson. On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems. Technical Report ORFE 99-01, Dept. of Operations Research and Financial Engineering, Princeton University, Princeton NJ, November 1999. http://citeseer.ist.psu.edu/vanderbei99formulating.html More
@techreport{ vanderbei99formulating,
author = "R. J. Vanderbei and H. Yurttan",
title = "On Formulating Semidefinite Programming Problems as Smooth Convex Nonlinear Optimization Problems",
number = "ORFE--99--01",
address = "Princeton, NJ",
year = "1999",
url = "citeseer.ist.psu.edu/vanderbei99formulating.html" }
Citations (may not include all citations):238 Nonnegative Matrices in the Mathematical Sciences (context) - Berman, Plemmons - 1979
94 LOQO: An interior point code for quadratic programming - Vanderbei - 1999
71 Solving large-scale sparse semidefinite programs for combina.. - Benson, Ye et al. - 1997
64 An interior-point algorithm for nonconvex nonlinear programm.. - Vanderbei, Shanno - 1999
48 Self--concordant functions and polynomial--time methods in c.. (context) - Nesterov, Nemirovsky - 1989
35 Handbook for Automatic Computation (context) - Wilkinson, Reinsch - 1971
33 Solving semidefinite programs via nonlinear programming part.. - Burer, Monteiro et al. - 1999
33 Solving semidefinite programs via nonlinear programming part.. - Burer, Monteiro et al. - 1999
28 Second derivatives for optimizing eigenvalues of symmetric m.. (context) - Overton, Womersley - 1993
19 A study of search directions in primal-dual interior-point m.. - Todd - 1999
15 Limiting behavior of the affine scaling continuous trajector.. (context) - Adler, Monteiro - 1991
10 A nonlinear programming problem in statistics (context) - Fletcher - 1981
5 ampl/nlmodels (context) - Vanderbei, http et al.
4 An algorithmic and numerical comparison of several interiorp.. (context) - Vanderbei, Duarte et al. - 1994
2 Symmetric decomposition of positive definite band matrices (context) - Martin, Wilkinson - 1965
1 Semi-definite matrix constaints in optimization (context) - Fletcher - 1985
1 An efficient algorithm for solving the max-cut (context) - Burer, Monteiro - 1998
1 VANDERBEI AND YURTTAN (context) - Lewis, Overton et al. - 1996
The graph only includes citing articles where the year of publication is known.
Documents on the same site (http://www.princeton.edu/~rvdb/techreps_ps.html): More
On The Symmetric Formulation Of Interior-Point Methods - Vanderbei, Yang (1994) (Correct)
LOQO: An Interior Point Code for Quadratic Programming - Vanderbei (1998) (Correct)
LOQO User's Manual - Version 2.27 - Vanderbei (1997) (Correct)
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