LPnetlib/lp_greenbeb

Netlib LP problem greenbeb: minimize c'*x, where Ax=b, lo<=x<=hi
Name lp_greenbeb
Group LPnetlib
Matrix ID 631
Num Rows 2,392
Num Cols 5,598
Nonzeros 31,070
Pattern Entries 31,070
Kind Linear Programming Problem
Symmetric No
Date 1984
Author K. Palmer
Editor R. Fourer
Structural Rank 2,389
Structural Rank Full false
Num Dmperm Blocks 75
Strongly Connect Components 9
Num Explicit Zeros 0
Pattern Symmetry 0%
Numeric Symmetry 0%
Cholesky Candidate no
Positive Definite no
Type real
SVD Statistics
Matrix Norm 1.062251e+02
Minimum Singular Value 7.842182e-64
Condition Number 1.354535e+65
Rank 2,389
sprank(A)-rank(A) 0
Null Space Dimension 3
Full Numerical Rank? no
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 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         
GREENBEB   2393   5405    31499     235739  B    -4.3021476065E+06        
                                                                          
        BOUND-TYPE TABLE                                                  
GREENBEB   UP LO FX FR                                                    
                                                                          
Supplied by Bob Fourer.                                                   
Empty RHS section.                                                        
When included in Netlib: Extra bound sets omitted,  extra free            
rows omitted.                                                             
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)                          
GREENBEB    -4.3022602612E+06    -4.3021537702E+06                        
                                                                          
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