Typical Linear Programming Problem

This example solves the typical linear programming problem

$$\underset{x}{\min }{f}^{T}xsuchthat\{\begin{array}{c}A\cdot x\le b,\\ Aeq\cdot x=beq,\\ x\ge 0.\end{array}$$

Load the sc50b.mat file, which is available when you run this example and contains the matrices and vectors A, Aeq, b, beq, f, and the lower bounds lb.

load sc50b

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

disp(size(A))

    30    48

disp(size(Aeq))

    20    48

Set options to use the dual-simplex algorithm and the iterative display.

options = optimoptions(@linprog,'Algorithm','dual-simplex','Display','iter');

The problem has no upper bound, so set ub to [].

ub = [];

Solve the problem by calling linprog.

[x,fval,exitflag,output] = ...
    linprog(f,A,b,Aeq,beq,lb,ub,options);

Running HiGHS 1.7.1: Copyright (c) 2024 HiGHS under MIT licence terms
Coefficient ranges:
  Matrix [3e-01, 3e+00]
  Cost   [1e+00, 1e+00]
  Bound  [0e+00, 0e+00]
  RHS    [3e+02, 3e+02]
Presolving model
37 rows, 37 cols, 93 nonzeros  0s
19 rows, 19 cols, 61 nonzeros  0s
15 rows, 15 cols, 65 nonzeros  0s
15 rows, 15 cols, 65 nonzeros  0s
Presolve : Reductions: rows 15(-35); columns 15(-33); elements 65(-53)
Solving the presolved LP
Using EKK dual simplex solver - serial
  Iteration        Objective     Infeasibilities num(sum)
          0    -8.6188168580e-01 Ph1: 10(11.7103); Du: 1(0.861882) 0s
         16    -7.0000000000e+01 Pr: 0(0) 0s
Solving the original LP from the solution after postsolve
Model   status      : Optimal
Simplex   iterations: 16
Objective value     : -7.0000000000e+01
HiGHS run time      :          0.02

Optimal solution found.

Examine the exit flag, objective function value at the solution, and number of iterations used by linprog to solve the problem.

exitflag,fval,output.iterations

exitflag = 
1

fval = 
-70.0000

ans = 
16

You can also find the objective function value and number of iterations in the iterative display.