## LPnetlib/lpi_greenbea

Netlib LP problem greenbea: minimize c'*x, where Ax=b, lo<=x<=hi

Name | lpi_greenbea |
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Group | LPnetlib |

Matrix ID | 718 |

Num Rows | 2,393 |

Num Cols | 5,596 |

Nonzeros | 31,074 |

Pattern Entries | 31,074 |

Kind | Linear Programming Problem |

Symmetric | No |

Date | 1988 |

Author | R. Fourer |

Editor | R. Fourer |

SVD Statistics | |
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Matrix Norm | 1.062251e+02 |

Minimum Singular Value | 4.062603e-64 |

Condition Number | 2.614705e+65 |

Rank | 2,390 |

sprank(A)-rank(A) | 0 |

Null Space Dimension | 3 |

Full Numerical Rank? | no |

Download Singular Values | MATLAB |

Download | MATLAB Rutherford Boeing Matrix Market |
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Notes |
A Netlib LP problem, in lp/data. For more information send email to netlib@ornl.gov with the message: send index from lp send readme from lp/data The following are relevant excerpts from lp/data/readme (by David M. Gay): The column and nonzero counts in the PROBLEM SUMMARY TABLE below exclude slack and surplus columns and the right-hand side vector, but include the cost row. We have omitted other free rows and all but the first right-hand side vector, as noted below. The byte count is for the MPS compressed file; it includes a newline character at the end of each line. These files start with a blank initial line intended to prevent mail programs from discarding any of the data. The BR column indicates whether a problem has bounds or ranges: B stands for "has bounds", R for "has ranges". The BOUND-TYPE TABLE below shows the bound types present in those problems that have bounds. The optimal value is from MINOS version 5.3 (of Sept. 1988) running on a VAX with default options. PROBLEM SUMMARY TABLE Name Rows Cols Nonzeros Bytes BR Optimal Value GREENBEA 2393 5405 31499 235711 B -7.2462405908E+07 BOUND-TYPE TABLE GREENBEA UP LO FX Supplied by Bob Fourer. When included in Netlib: Extra bound sets omitted; Extra free rows omitted. Empty RHS section. Problems GREENBEA and GREENBEB differ only in their BOUNDS sections. Bob Bixby reports that the CPLEX solver (running on a Sparc station) finds slightly different optimal values for some of the problems. On a MIPS processor, MINOS version 5.3 (with crash and scaling of December 1989) also finds different optimal values for some of the problems. The following table shows the values that differ from those shown above. (Whether CPLEX finds different values on the recently added problems remains to be seen.) Problem CPLEX(Sparc) MINOS(MIPS) GREENBEA -7.2555248130E+07 Source: GREENBEA, GREENBEB: a large refinery model; see the book "A Model-Management Framework for Mathematical Programming" by Kenneth H. Palmer et al. (John Wiley & Sons, New York, 1984). Added to Netlib on 6 May 1988 |