## LPnetlib/lp_etamacro

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

Name | lp_etamacro |
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Group | LPnetlib |

Matrix ID | 621 |

Num Rows | 400 |

Num Cols | 816 |

Nonzeros | 2,537 |

Pattern Entries | 2,537 |

Kind | Linear Programming Problem |

Symmetric | No |

Date | |

Author | M. Saunders |

Editor | D. Gay |

SVD Statistics | |
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Matrix Norm | 2.258292e+03 |

Minimum Singular Value | 4.297841e-02 |

Condition Number | 5.254481e+04 |

Rank | 400 |

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

Null Space Dimension | 0 |

Full Numerical Rank? | yes |

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 send minos 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 ETAMACRO 401 688 2489 21915 B -7.5571521774E+02 BOUND-TYPE TABLE ETAMACRO UP LO FX From Michael Saunders, Systems Optimization Laboratory at Stanford University. When included in Netlib: Cost coefficients negated. 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) ETAMACRO -7.5571523337E+02 -7.5571522100E+02 The following are relevant excerts from lp/data/minos (by Michael Saunders), regarding experience with MINOS 5.0 on the problems he provided: (unscaled) (scaled) File Name Rows Cols Elems Optimal Objective Itns Time Itns Time ---- -------- ---- ---- ----- ----------------- ---- ---- ---- ---- 12. ETAMACRO 401 689 2489 7.5571521E+02 MAX 904 15.0 927 17.6 * Objective is the first row of type N. It is minimized except as shown. * Itns is the number of iterations required to solve the problem by the primal simplex method, as implemented in the Fortran code MINOS 5.0 (May 1985), using default values for all parameters. (The initial basis is triangular.) * Time is the processor time required on an IBM 3081K. The MINOS source code was compiled with the IBM Fortran 77 compiler VS FORTRAN, using the options NOSDUMP, NOSYM and OPT(3). |