LPnetlib/lp_scagr7
Netlib LP problem scagr7: minimize c'*x, where Ax=b, lo<=x<=hi
Name 
lp_scagr7 
Group 
LPnetlib 
Matrix ID 
669 
Num Rows

129 
Num Cols

185 
Nonzeros

465 
Pattern Entries

465 
Kind

Linear Programming Problem 
Symmetric

No 
Date

1981 
Author

J. Ho, E. Loute 
Editor

R. Fourer 
Structural Rank 
129 
Structural Rank Full 
true 
Num Dmperm Blocks

2 
Strongly Connect Components

1 
Num Explicit Zeros

0 
Pattern Symmetry

0% 
Numeric Symmetry

0% 
Cholesky Candidate

no 
Positive Definite

no 
Type

real 
SVD Statistics 
Matrix Norm 
1.026117e+01 
Minimum Singular Value 
1.723961e01 
Condition Number 
5.952091e+01

Rank 
129 
sprank(A)rank(A) 
0 
Null Space Dimension 
0 
Full Numerical Rank? 
yes 
Download Singular Values 
MATLAB

Download 
MATLAB
Rutherford Boeing
Matrix Market

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 righthand side vector, but include
the cost row. We have omitted other free rows and all but the first
righthand 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 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
SCAGR7 130 140 553 4953 2.3313892548E+06
Supplied by Bob Fourer.
Source: J.K. Ho and E. Loute, "A Set of Staircase Linear Programming
Test Problems", Math. Prog. 20 (1981), pp. 245250.
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)
SCAGR7 2.3313898243E+06 2.3313897524E+06
