%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/lp_pilot
% name: LPnetlib/lp_pilot
% [Netlib LP problem pilot: minimize c'*x, where Ax=b, lo<=x<=hi]
% id: 654
% date: 1989
% author: M. Saunders
% ed: D. Gay
% fields: title name A b id aux kind date author ed notes
% aux: c lo hi z0
% kind: linear programming problem
%-------------------------------------------------------------------------------
% 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             
% 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.                                             
%                                                                               
%-------------------------------------------------------------------------------
