%-------------------------------------------------------------------------------
% UF Sparse Matrix Collection, Tim Davis
% http://www.cise.ufl.edu/research/sparse/matrices/LPnetlib/lp_stair
% name: LPnetlib/lp_stair
% [Netlib LP problem stair: minimize c'*x, where Ax=b, lo<=x<=hi]
% id: 691
% date: 
% 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                                                     
%                                                                               
% ------------------------------------------------------------------------------
% This LP problem is the source of four sparse matrices in the Harwell/Boeing   
% sparse matrix collection: STR_0, STR_200, STR_400, and STR_600.  Those four   
% matrices are square, nonsingular basis matrices that occured during the       
% solution of STAIR.                                                            
% ------------------------------------------------------------------------------
%                                                                               
% 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             
% STAIR       357    467     3857      27405  B    -2.5126695119E+02            
%                                                                               
%         BOUND-TYPE TABLE                                                      
% STAIR      UP    FX FR                                                        
%                                                                               
% From Michael Saunders, Systems Optimization Laboratory at Stanford University.
% When included in Netlib: Explicit zeros omitted;                              
% cost coefficients negated.                                                    
%                                                                               
% 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   
% ---- --------  ----  ----  -----  -----------------  ----  ----  ----  ----   
%  11. STAIR      357   467   3867  2.5126695E+02 MAX   519  15.7   389  13.1   
%                                                                               
% * 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).         
%                                                                               
%-------------------------------------------------------------------------------
