Reliable Outer Bounds for the Dual Simplex Algorithm with Interval Right-hand Side

6533b82ffe1ef96bd1294d78

RESEARCH PRODUCT

Reliable Outer Bounds for the Dual Simplex Algorithm with Interval Right-hand Side

Fuenfzig Christoph Dominique Michelucci Foufou Sebti

subject

verified simplex algorithm [INFO.INFO-RO] Computer Science [cs]/Operations Research [cs.RO][ INFO.INFO-NA ] Computer Science [cs]/Numerical Analysis [cs.NA][INFO.INFO-NA] Computer Science [cs]/Numerical Analysis [cs.NA]tableau form [INFO.INFO-RO]Computer Science [cs]/Operations Research [cs.RO][INFO.INFO-NA]Computer Science [cs]/Numerical Analysis [cs.NA]interval arithmetic OpenMP parallelization [ INFO.INFO-RO ] Computer Science [cs]/Operations Research [cs.RO]

description

International audience; In this article, we describe the reliable computation of outer bounds for linear programming problems occuring in linear relaxations derived from the Bernstein polynomials. The computation uses interval arithmetic for the Gauss-Jordan pivot steps on a simplex tableau. The resulting errors are stored as interval right hand sides. Additionally, we show how to generate a start basis for the linear programs of this type. We give details of the implementation using OpenMP and comment on numerical experiments.

year	journal	country	edition	language
2013-09-30

https://hal.archives-ouvertes.fr/hal-00927168

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