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Abstract: Semidefinite programming (SDP) is a convex optimization problem in the space of symmetric matrices. Primal-dual interior-point methods for SDP are discussed. These generate primal and dual matrices X and Z which commute only in the limit. A new method is proposed which iterates in the space of commuting matrices. Let S! n\Thetan denote the set of real symmetric n \Theta n matrices. The standard inner product on this space is A ffl B = tr AB = P i;j a ij b ij : By X 0, where X 2 S!... (Update)
Context of citations to this paper: More
.... in [8, 9] The NT method was given in [13, 12] and its implementation was recently discussed in [16] The Q method originally appeared in [1]. Many other papers on semidefinite programming have recently been announced. The paper is organized as follows. In section 2 we...
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14: An interior-- point method for semidefinite programming - Helmberg, Rendl et al. - 1996
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BibTeX entry: (Update)
F. ALIZADEH, J.A. HAEBERLY, and M.L. OVERTON. A new primal-dual Interiorpoint method for semidefinite programming. to appear in: Proceedings of the Fifth SIAM Conference on Appl. Linear Algebra, Snowbird, Utah, June 1994. http://citeseer.ist.psu.edu/alizadeh94new.html More
@incollection{ alizadeh94new,
author = "F. Alizadeh and J.--P. A. Haeberly and M. L. Overton",
title = "A new primal--dual interior--point method for semidefinite programming",
booktitle = "Applied Linear Algebra (Proceedings of the 5th {SIAM} Conference, held in Snowbird, {UT}, {USA}, June 1994)",
publisher = "SIAM Publications",
address = "Philadelphia, PA, USA",
editor = "J. G. Lewis",
pages = "113--117",
year = "1994",
url = "citeseer.ist.psu.edu/alizadeh94new.html" }
Citations (may not include all citations):326 Interior Point Polynomial Algorithms in Convex Programming (context) - Nesterov, Nemirovskii - 1994
230 Interior point methods in semidefinite programming with appl.. - Alizadeh - 1994
98 the implementation of a primal-dual interior point method (context) - Mehrotra - 1992
90 Primal-dual potential reduction method for problems involvin.. - Vandenberghe, Boyd - 1994
68 Interior point methods for linear programming: Computational.. (context) - Lustig, Marsten et al. - 1994
60 Combinatorial Optimization with Interior Point Methods and S.. (context) - Alizadeh - 1991
43 the superlinear and quadratic convergence of primal-dual int.. (context) - Zhang, Tapia et al. - 1992
35 Symmetric indefinite systems for interior-point methods (context) - Vanderbei, Carpenter - 1993
30 A primal-dual interior point method for linear programming (context) - Kojima, Mizuno et al. - 1989
28 Second derivatives for optimizing eigenvalues of symmetric m.. (context) - Overton, Womersley - 1993
13 Optimal design of nonlinear shell structures (context) - Ringertz - 1991
9 primal-dual interior point algorithms (context) - Rendl, Vanderbei et al. - 1993
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