The LP-Newton method for standard form linear programming problems

Tomonari Kitahara; Shinji Mizuno; Jianming Shi

doi:10.1016/j.orl.2013.05.004

The LP-Newton method for standard form linear programming problems

Tomonari Kitahara, Shinji Mizuno, Jianming Shi

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Fujishige et al. propose the LP-Newton method, a new algorithm for solving linear programming problems (LPs). They address LPs which have a lower and an upper bound for each variable. They reformulate the problem by introducing a related zonotope. Their algorithm solves the problem by repeating projections to the zonotope. In this paper, we develop the LP-Newton method for solving standard form LPs. We recast the LP by introducing a related convex cone. Our algorithm solves the problem by iterating projections to the convex cone.

Original language	English
Pages (from-to)	426-429
Number of pages	4
Journal	Operations Research Letters
Volume	41
Issue number	5
DOIs	https://doi.org/10.1016/j.orl.2013.05.004
Publication status	Published - 2013
Externally published	Yes

All Science Journal Classification (ASJC) codes

Software
Management Science and Operations Research
Industrial and Manufacturing Engineering
Applied Mathematics

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10.1016/j.orl.2013.05.004

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AU - Mizuno, Shinji

AU - Shi, Jianming

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AB - Fujishige et al. propose the LP-Newton method, a new algorithm for solving linear programming problems (LPs). They address LPs which have a lower and an upper bound for each variable. They reformulate the problem by introducing a related zonotope. Their algorithm solves the problem by repeating projections to the zonotope. In this paper, we develop the LP-Newton method for solving standard form LPs. We recast the LP by introducing a related convex cone. Our algorithm solves the problem by iterating projections to the convex cone.

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JO - Operations Research Letters

JF - Operations Research Letters

IS - 5

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The LP-Newton method for standard form linear programming problems

Abstract

All Science Journal Classification (ASJC) codes

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