I am using the linprog function in Matlab to solve a set of large linear programming problems. I have 2601 decision variables, 51 inequality constraints, 71 equality constraints, and lower bounds of 0 for all variables.
The coefficients in the objective function and constraints vary in different problems. I am using the simplex method (when I try active-set and interior-point the program never stops running, as long as I have waited which was more than hours).
The simplex method converges for some of the problems very quickly, and for some of them (also very quickly) shows this message:
Exiting: The constraints are overly stringent; no feasible starting point found.
However, even for the ones with that message, it still provides a solution which satisfy the constraints. Can I just ignore that message and use the solutions or the message is important and the solution is probably not optimum?
Update: It turned out that the interior-point method solves some of them, but not the others. So in the code below, I used the interior-point method for the ones that work with it, and the simplex method with the rest.
These are my files and this is my code:
clc; clear;
%distances
t1 = readtable('t.xlsx', 'ReadVariableNames',false);
ti = table2array(t1);
sz = size(ti);
tiv = reshape(ti, [1,sz(1)*sz(2)]);
%crude oil production and attraction
A = readtable('A.xlsx', 'ReadVariableNames',false);
Ai = table2array(A);
P = readtable('P.xlsx', 'ReadVariableNames',false);
Pi = table2array(P);
%others
one1 = readtable('A Matrix.xlsx', 'ReadVariableNames',false);
one = table2array(one1);
two1 = readtable('Aeq Matrix.xlsx', 'ReadVariableNames',false);
two = table2array(two1);
zero = zeros(sz(1), sz(1));
infin = inf(sz(1), sz(1));
zerov = reshape(zero, [1,sz(1)*sz(2)]);
infinv = reshape(infin, [1,sz(1)*sz(2)]);
%OF
f = (tiv).^1;
%linear program
%x = linprog(f,A,b,Aeq,beq,lb,ub)
options1 = optimoptions('linprog','Algorithm','interior-point');
options2 = optimoptions('linprog','Algorithm','simplex');
x1999 = vec2mat(linprog(f,one,Pi(1,1:end),two,Ai(1,1:end),zerov,infinv,zerov,options2),sz(1));
x2000 = vec2mat(linprog(f,one,Pi(2,1:end),two,Ai(2,1:end),zerov,infinv,zerov,options1),sz(1));
x2001 = vec2mat(linprog(f,one,Pi(3,1:end),two,Ai(3,1:end),zerov,infinv,zerov,options1),sz(1));
x2002 = vec2mat(linprog(f,one,Pi(4,1:end),two,Ai(4,1:end),zerov,infinv,zerov,options1),sz(1));
x2003 = vec2mat(linprog(f,one,Pi(5,1:end),two,Ai(5,1:end),zerov,infinv,zerov,options1),sz(1));
x2004 = vec2mat(linprog(f,one,Pi(6,1:end),two,Ai(6,1:end),zerov,infinv,zerov,options1),sz(1));
x2005 = vec2mat(linprog(f,one,Pi(7,1:end),two,Ai(7,1:end),zerov,infinv,zerov,options1),sz(1));
x2006 = vec2mat(linprog(f,one,Pi(8,1:end),two,Ai(8,1:end),zerov,infinv,zerov,options1),sz(1));
x2007 = vec2mat(linprog(f,one,Pi(9,1:end),two,Ai(9,1:end),zerov,infinv,zerov,options2),sz(1));
x2008 = vec2mat(linprog(f,one,Pi(10,1:end),two,Ai(10,1:end),zerov,infinv,zerov,options2),sz(1));
x2009 = vec2mat(linprog(f,one,Pi(11,1:end),two,Ai(11,1:end),zerov,infinv,zerov,options2),sz(1));
x2010 = vec2mat(linprog(f,one,Pi(12,1:end),two,Ai(12,1:end),zerov,infinv,zerov,options2),sz(1));
x2011 = vec2mat(linprog(f,one,Pi(13,1:end),two,Ai(13,1:end),zerov,infinv,zerov,options2),sz(1));
x2012 = vec2mat(linprog(f,one,Pi(14,1:end),two,Ai(14,1:end),zerov,infinv,zerov,options1),sz(1));
x2013 = vec2mat(linprog(f,one,Pi(15,1:end),two,Ai(15,1:end),zerov,infinv,zerov,options2),sz(1));
x2014 = vec2mat(linprog(f,one,Pi(16,1:end),two,Ai(16,1:end),zerov,infinv,zerov,options2),sz(1));
x2015 = vec2mat(linprog(f,one,Pi(17,1:end),two,Ai(17,1:end),zerov,infinv,zerov,options2),sz(1));
x2016 = vec2mat(linprog(f,one,Pi(18,1:end),two,Ai(18,1:end),zerov,infinv,zerov,options1),sz(1));
In case somebody wants to know what the problem was, I found that for those programs with error, there was actually no feasible point and what the error said was correct. I found it out by running the same linear programs with a vector of zeros for the objective function's coefficients, and getting the same error (recommended method by Matlab's manual).