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xlinprog

Home | intlinprog help page

linprog function

Linear Programming Solver linprog can solve Linear Programming minimization problems with the GLPK function.

Therefore, it can solve min f'*x subject to the constraints

A*x<=b
Aeq*x=beq
lb<=x<=ub

Syntax

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

Input arguments

f: A column array containing the objective function coefficients.

A: A matrix containing the inequality constraints.

b: A column array containing the right-hand side value for each inequality constraint in the A matrix.

Aeq: A matrix containing the equality constraints.

beq: A column array containing the right-hand side value for each equality constraint in the Aeq matrix.

lb: An array containing the lower bound on each of the variables. If lb is not supplied, the default lower bound for the variables is zero.

ub: An array containing the upper bound on each of the variables. If ub is not supplied, the default upper bound is assumed to be infinite.

options: Optimization options, generated as the output of optimoptions. The available options are listed below:

Option Name Option Description
Algorithm
  • 'dual-simplex' (default)
  • 'interior-point-legacy'
  • 'interior-point'
Display
  • 'final' (default) displays just the final output.
  • 'off' or 'none' displays no output.
  • 'iter' displays output at each iteration.
MaxIterations Simplex iterations limit. It is decreased by one each time when one simplex iteration has been performed, and reaching zero value signals the solver to stop the search.
MaxTime Searching time limit, in milliseconds.
Preprocess If 'basic', the simplex solver uses the built-in LP presolver. If 'none', the LP presolver is not used.

Output arguments

x: The optimizer (the value of the decision variables at the optimum).

fval: The optimum value of the objective function.

exitflag: Reason linprog stopped, returned as an integer. The available exitflags are listed below:

Error Code Error Description
1 Function converged to a solution x.
0 Number of iterations exceeded options.MaxIterations or solution time in seconds exceeded options.MaxTime.
-2 No feasible point was found.
-3 Problem is unbounded.
-4 NaN value was encountered during execution of the algorithm.
-5 Both primal and dual problems are infeasible.
-7 Search direction became too small. No further progress could be made.
-9 Solver lost feasibility.
-99 Other error - see extra

output: Information about the optimization process, returned as a structure with the following fields:

Output Name Output Description
message Exit message
error_message GLPK exitflag message