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Published in: Numerical Algorithms 3/2021

27-04-2020 | Original Paper

Extension of the LP-Newton method to conic programming problems via semi-infinite representation

Authors: Mirai Tanaka, Takayuki Okuno

Published in: Numerical Algorithms | Issue 3/2021

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Abstract

The LP-Newton method solves linear programming (LP) problems by repeatedly projecting a current point onto a certain relevant polytope. In this paper, we extend the algorithmic framework of the LP-Newton method to conic programming (CP) problems via a linear semi-infinite programming (LSIP) reformulation. In this extension, we produce a sequence by projection onto polyhedral cones constructed from LP problems obtained by finitely relaxing the LSIP problem equivalent to the CP problem. We show global convergence of the proposed algorithm under mild assumptions. To investigate its efficiency, we apply our proposed algorithm and a primal-dual interior-point method to second-order cone programming problems and compare the obtained results.

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Metadata
Title
Extension of the LP-Newton method to conic programming problems via semi-infinite representation
Authors
Mirai Tanaka
Takayuki Okuno
Publication date
27-04-2020
Publisher
Springer US
Published in
Numerical Algorithms / Issue 3/2021
Print ISSN: 1017-1398
Electronic ISSN: 1572-9265
DOI
https://doi.org/10.1007/s11075-020-00933-6

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