Polynomial primal-dual cone affine scaling for semidefinite programming
نویسندگان
چکیده
منابع مشابه
Polynomial Primal Dual Cone Affine Scaling for Semidefinite Programming
Semide nite programming concerns the problem of optimizing a linear function over a section of the cone of semide nite matrices In the cone a ne scaling approach we replace the cone of semide nite matrices by a certain inscribed cone in such a way that the resulting optimization problem is analytically solvable The now easily obtained solution to this modi ed problem serves as an approximate so...
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Two primal{dual a ne scaling algorithms for linear programming are extended to semide nite programming. The algorithms do not require (nearly) centered starting solutions, and can be initiated with any primal{dual feasible solution. The rst algorithm is the Dikin-type a ne scaling method of Jansen et al. [8] and the second the pure a ne scaling method of Monteiro et al. [12]. The extension of t...
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In this paper, we give an example of a semidefinite programming problem in which primal-dual affine-scaling algorithms using the HRVW/KSH/M, MT, and AHO directions fail. We prove that each of these algorithm can generate a sequence converging to a non-optimal solution, and that, for the AHO direction, even its associated continuous trajectory can converge to a non-optimal point. In contrast wit...
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Copies of these reports may be obtained from the bureau of the Faculty of Technical Math-A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract Primal{dual aane{scaling methods have recently been extended from linear programming to semideenite programming. We show how to analyse these methods in the framework of potential reduction algorithms. The a...
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In this paper we introduce a primal-dual affine scaling method. The method uses a search-direction obtained by minimizing the duality gap over a linearly transformed conic section. This direction neither coincides with known primal-dual affine scaling directions (Jansen et al., 1993; Monteiro et al., 1990), nor does it fit in the generic primal-dual method (Kojima et al., 1989). The new method ...
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ژورنال
عنوان ژورنال: Applied Numerical Mathematics
سال: 1999
ISSN: 0168-9274
DOI: 10.1016/s0168-9274(98)00100-7