Typical Linear Programming Problem

This example shows the solution of a typical linear programming problem. The problem is

minxfTx such that {Axb,Aeqx=beq,x0.

You can load the matrices and vectors A, Aeq, b, beq, f, and the lower bounds lb into the MATLAB® workspace with

load sc50b

The problem in sc50b.mat has 48 variables, 30 inequalities, and 20 equalities.

Use linprog to solve the problem:

options = optimoptions(@linprog,'Algorithm','dual-simplex','Display','iter');
[x,fval,exitflag,output] = ...
    linprog(f,A,b,Aeq,beq,lb,[],options);

Because the iterative display was set using optimoptions, the results displayed are

LP preprocessing removed 2 inequalities, 16 equalities,
16 variables, and 26 non-zero elements.

 Iter      Time            Fval  Primal Infeas    Dual Infeas  
    0     0.001    0.000000e+00   0.000000e+00   1.305013e+00  
    8     0.001   -1.587073e+02   3.760622e+02   0.000000e+00  
   33     0.001   -7.000000e+01   0.000000e+00   0.000000e+00

Optimal solution found.

The exitflag value is positive, telling you linprog converged. You can also get the final function value in fval and the number of iterations in output.iterations:

exitflag,fval,output

exitflag =

     1


fval =

   -70


output = 

  struct with fields:

         iterations: 33
    constrviolation: 3.1264e-13
            message: 'Optimal solution found.'
          algorithm: 'dual-simplex'
      firstorderopt: 2.3082e-14