Computational Experience with Rigorous Error Bounds for the Netlib Linear Programming Library

Keil, Christian; Jansson, Christian

doi:10.1007/s11155-006-9004-7

Cited by 15 publications

(14 citation statements)

References 13 publications

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“…In particular, for certain nonsmooth problems and ill-conditioned or ill-posed problems, the algorithm may quit when UF * − LF * < and the box containing the point x at which f (x) = UF * may be printed; the other boxes need not be further resolved or verified. Christian Keil and Christian Jansson [108] have been successful at handling a variety of difficult test problems from the Netlib LP test set 44 with this criterion. Basically, this process first uses an efficient commercial or open-source solver to compute an approximate solution with floating point arithmetic.…”

Section: Pitfalls and Clarificationsmentioning

confidence: 99%

Introduction to Interval Analysis

Moore¹,

Kearfott²,

Cloud³

2009

1,779

1,126

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Of the various interval-based software packages that are available, we chose INTLAB for several reasons. It is fully integrated into the interactive, programmable, and highly popular MATLAB system. It is carefully written, with all basic interval computations represented. Finally, both MATLAB and INTLAB code can be written in a fashion that is clear and easy to debug. We wish to cordially thank George Corliss, Andreas Frommer, and Siegfried Rump, as well as the anonymous reviewers, for their many constructive comments. We owe Siegfried Rump additional thanks for developing INTLAB and granting us permission to use it in this book.

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Section: Pitfalls and Clarificationsmentioning

confidence: 99%

Introduction to Interval Analysis

Moore¹,

Kearfott²,

Cloud³

2009

1,779

1,126

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“…Here we present a summary of our numerical results for the NETLIB suite of linear programming problems [33]. For details refer to [23]. The NETLIB collection contains problems with up to 15695 variables and 16675 constraints.…”

Section: Certificate Of Infeasibility In Branch and Bound Algorithmsmentioning

confidence: 99%

Rigorous Error Bounds for the Optimal Value in Semidefinite Programming

Jansson¹,

Chaykin²,

Keil³

2008

SIAM J. Numer. Anal.

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A wide variety of problems in global optimization, combinatorial optimization as well as systems and control theory can be solved by using linear and semidefinite programming. Sometimes, due to the use of floating point arithmetic in combination with ill-conditioning and degeneracy, erroneous results may be produced. The purpose of this article is to show how rigorous error bounds for the optimal value can be computed by carefully postprocessing the output of a linear or semidefinite programming solver. It turns out that in many cases the computational costs for postprocessing are small compared to the effort required by the solver. Numerical results are presented including problems from the SDPLIB and the NETLIB LP library; these libraries contain many ill-conditioned and real life problems.

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“…These problems are illposed in the sense of Hadamard; we used the measure in [38] and found that 71% of the problems have infinite condition number. (See also [29].) In particular, small changes in the data can result in large changes in the optimum x, y, z, see e.g.…”

Section: Netlib Set-ill-conditioned Problemsmentioning

confidence: 99%