linprog

📝Syntax

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

📥Input Arguments

Parameter	Description
f	linear objective coefficients.
A, b	linear inequality constraints A*x <= b.
Aeq, beq	linear equality constraints Aeq*x = beq.
lb, ub	lower and upper variable bounds.
options	solver options created with optimoptions or optimset.

📤Output Arguments

Parameter	Description
x	computed minimizer.
fval	objective value f'*x.
exitflag	termination indicator.
output	diagnostic structure.
lambda	structure with lower, upper, ineqlin and eqlin multiplier estimates.

📄Description

linprog solves linear optimization problems with linear constraints and bounds. Nelson uses HiGHS when available.

Supported structures include f, Aineq or A, bineq or b, Aeq, beq, lb, ub, x0 and options. The output structure reports the algorithm, normalized backend status, primal solution status, message, constraint violation, iterations and first-order residual estimate. The lambda structure is filled for continuous linear programs from backend dual information.

Options such as Display, MaxTime, MaxIterations, LPMaxIterations, ConstraintTolerance, LPOptimalityTolerance, LPPreprocess and RootLPAlgorithm are converted to HiGHS options when possible. Other recognized optimization options are accepted and ignored when no backend equivalent exists.

💡Examples

f = [-1; -1];
A = [1 2; 4 2];
b = [4; 12];
opts = optimoptions('linprog', 'Display', 'off');
[x, fval, exitflag, output, lambda] = linprog(f, A, b, [], [], [0; 0], [], opts)

🔗See Also

intlinprog quadprog optimoptions

Used Functions

optimoptions prob2struct

📚Bibliography

Dantzig, G. B., Linear Programming and Extensions, Princeton University Press, 1963. Huangfu, Q. and Hall, J. A. J., Parallelizing the dual revised simplex method, Mathematical Programming Computation, 2018. Nocedal, J. and Wright, S. J., Numerical Optimization, Springer, 2006.