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Typical Linear Programming Problem
This example solves the typical linear programming problem
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 1.7.0: 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 : 0.01 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.