A scaled Gauss--Newton primal-dual search direction for semidefinite optimization (Q2706359)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A scaled Gauss--Newton primal-dual search direction for semidefinite optimization |
scientific article |
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19 March 2001
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semidefinite optimization
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primal-dual search directions
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interior point algorithms
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worst-case iteration complexity
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Gausss-Newton direction
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scaling
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least squares
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0.9268881
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0.9031004
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0.8872969
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0.8858769
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0.8856139
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0.8846848
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A scaled Gauss--Newton primal-dual search direction for semidefinite optimization (English)
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The authors present a primal-dual scaled Gauss-Newton direction for semidefinite optimization which allows polynomial worst-case iteration complexity analysis. This analysis was inspired by the Gausss-Newton direction studied by \textit{S. Kruk, M. Muramatsu, F. Rendl, R. J. Vanderbei} and \textit{H. Wolkowicz} [The Gauss-Newton direction in semidefinite programming, Research Report CORR 98-16, University of Waterloo, Dept. Combinatorics and Optimization, Waterloo, Canada (1998)] but the new direction seems much more amenable to complexity analysis, due to the use of scaling and a local norm in the definition of the least squares problem. In particular, the usual \(O(\sqrt n)\) iteration complexity is derived in this paper for the standard small update primal-dual path following algorithms.
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