Matrix: LPnetlib/lp_pilot

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

LPnetlib/lp_pilot graph
(bipartite graph drawing)

LPnetlib/lp_pilot dmperm of LPnetlib/lp_pilot

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  • Matrix group: LPnetlib
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  • download as a MATLAB mat-file, file size: 197 KB. Use UFget(654) or UFget('LPnetlib/lp_pilot') in MATLAB.
  • download in Matrix Market format, file size: 202 KB.
  • download in Rutherford/Boeing format, file size: 127 KB.

    Matrix properties
    number of rows1,441
    number of columns4,860
    structural full rank?yes
    structural rank1,441
    # of blocks from dmperm2
    # strongly connected comp.1
    explicit zero entries0
    nonzero pattern symmetry 0%
    numeric value symmetry 0%
    Cholesky candidate?no
    positive definite?no

    authorM. Saunders
    editorD. Gay
    kindlinear programming problem
    2D/3D problem?no

    Additional fieldssize and type
    bfull 1441-by-1
    cfull 4860-by-1
    lofull 4860-by-1
    hifull 4860-by-1
    z0full 1-by-1


    A Netlib LP problem, in lp/data.  For more information                        
    send email to 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             
    PILOT      1442   3652    43220     278593  B    -5.5740430007E+02            
            BOUND-TYPE TABLE                                                      
    PILOT      UP LO FX                                                           
    From Michael Saunders, Systems Optimization Laboratory at Stanford University.
    When included in Netlib: Extra bound sets omitted;                            
    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)                              
    PILOT       -5.5748972928E+02    -5.5741215293E+02                            
    Concerning PILOT87, Irv Lustig says, "PILOT87 is considered (by John          
    Stone, at least) to be harder than PILOT because of the bad scaling in        
    the numerics."                                                                
    Modified on Oct. 1991 (minor cleanup): removed 8 duplicate right-hand         
    side values for row BTRB01.                                                   
    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   
    ---- --------  ----  ----  -----  -----------------  ----  ----  ----  ----   
     13. PILOT     1460  3652  43645  5.5742994E+02 MAX    ?     ?  20000* 2hrs*  
    * 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).         
    * PILOT      is a linearized form of a quadratic program.  The first 45       
                 objective elements are the optimal gradients of the quadratic    
                 terms in the objective of the QP.  PILOT is normally solved      
                 from an advanced basis, with scaling.  The Itns and Time shown   
                 above are estimates.                                             

    Ordering statistics:result
    nnz(V) for QR, upper bound nnz(L) for LU, with COLAMD1,367,157
    nnz(R) for QR, upper bound nnz(U) for LU, with COLAMD180,661

    SVD-based statistics:
    null space dimension0
    full numerical rank?yes

    singular values (MAT file):click here
    SVD method used:s = svd (full (A)) ;

    LPnetlib/lp_pilot svd

    For a description of the statistics displayed above, click here.

    Maintained by Tim Davis, last updated 12-Mar-2014.
    Matrix pictures by cspy, a MATLAB function in the CSparse package.
    Matrix graphs by Yifan Hu, AT&T Labs Visualization Group.