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Semidefinite Programming by Perceptron Learning

Semidefinite Programming by Perceptron Learning
Semidefinite Programming by Perceptron Learning
We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasible region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.
Semidefinite programming, perceptron learning, optimization, probabilistic algorithm, MAXCUT.
0262201526
457-465
MIT Press
Graepel, Thore
f01fa538-c0f8-4e36-bbcc-698366e73f39
Herbrich, Ralf
3024ba7e-f3a1-4187-8655-b7f163c7c733
Kharechko, Andriy
9dccd719-b3fd-4ff6-9b85-b329e31cba9e
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Thrun, Sebastian
Saul, Lawrence
Scholkopf, Bernhard
Graepel, Thore
f01fa538-c0f8-4e36-bbcc-698366e73f39
Herbrich, Ralf
3024ba7e-f3a1-4187-8655-b7f163c7c733
Kharechko, Andriy
9dccd719-b3fd-4ff6-9b85-b329e31cba9e
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Thrun, Sebastian
Saul, Lawrence
Scholkopf, Bernhard

Graepel, Thore, Herbrich, Ralf, Kharechko, Andriy and Shawe-Taylor, John (2004) Semidefinite Programming by Perceptron Learning. In, Thrun, Sebastian, Saul, Lawrence and Scholkopf, Bernhard (eds.) Advances in Neural Information Processing Systems 16. MIT Press, pp. 457-465.

Record type: Book Section

Abstract

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasible region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.

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More information

Published date: 2004
Additional Information: Chapter: 8 Address: Cambridge, MA
Keywords: Semidefinite programming, perceptron learning, optimization, probabilistic algorithm, MAXCUT.
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 259597
URI: http://eprints.soton.ac.uk/id/eprint/259597
ISBN: 0262201526
PURE UUID: 07f3fdef-6ac4-40e2-87a7-4a2df2a01307

Catalogue record

Date deposited: 03 Aug 2004
Last modified: 14 Mar 2024 06:27

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Contributors

Author: Thore Graepel
Author: Ralf Herbrich
Author: Andriy Kharechko
Author: John Shawe-Taylor
Editor: Sebastian Thrun
Editor: Lawrence Saul
Editor: Bernhard Scholkopf

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