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Abstract: We study the semidefinite programming problem (SDP), i.e the problem of optimization of a linear function of a symmetric matrix subject to linear equality constraints and the additional condition that the matrix be positive semidefinite. First we review the classical cone duality as specialized to SDP. Next we present an interior point algorithm which converges to the optimal solution in polynomial time. The approach is a direct extension of Ye's projective method for linear programming. We... (Update)
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BibTeX entry: (Update)
F. ALIZADEH. Interior point methods in semidefinite programming with applications to combinatorial optimization. SIAM Journal on Optimization, 5:13--51, 1995. http://citeseer.ist.psu.edu/article/alizadeh93interior.html More
@article{ alizadeh95interior,
author = "F. Alizadeh",
title = "Interior Point Methods in Semidefinite Programming with Applications to Combinatorial Optimization",
journal = "SIAM Journal on Optimization",
volume = "5",
number = "1",
pages = "13--51",
year = "1995",
url = "citeseer.ist.psu.edu/article/alizadeh93interior.html" }
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448 A New Polynomial-Time Algorithm for Linear Programming (context) - Karmarkar - 1984 ACM DBLP
333 Geometric Algorithms and Combinatorial Optimization (context) - Grotschel, Lov'asz et al. - 1988
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49 Large-scale optimization of eigenvalues - Overton - 1992 ACM
49 An interior-point method for minimizing the maximum eigenval.. (context) - Jarre - 1991 ACM
48 Self-Concordant Functions and Polynomial Time Methods in Con.. (context) - Nesterov, Nemirovskii - 1990
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46 Laplacian eigenvalues and the maximum cut problem (context) - Delorme, Poljak - 1990 ACM
41 Polynomial-time primal-dual affine scaling algorithm for lin.. - Monteiro, Adler - 1988
41 A projection technique for partitioning the nodes of a graph - Rendl, Wolkowicz - 1993
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3 Facial reduction for a cone-convex programming problem (context) - Borwein, Wolkowicz - 1981
3 Sums of Singular Values (context) - Subramani - 1993
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