intlinprog

📝Syntax

x = intlinprog(f, intcon, A, b)
[x, fval, exitflag, output] = intlinprog(f, intcon, A, b, Aeq, beq, lb, ub, x0, options)
[x, fval, exitflag, output] = intlinprog(problem)

📥Input Arguments

Parameter	Description
f	linear objective coefficients.
intcon	indices of integer variables.
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.

📄Description

intlinprog solves linear optimization problems where selected variables are integer-valued. Nelson uses HiGHS when available.

The accepted problem structure can contain solver, f, intcon, Aineq or A, bineq or b, Aeq, beq, lb, ub, x0 and options fields.

The output structure reports relative and absolute gap, number of feasible points, node count, constraint violation, iterations, elapsed time, algorithm, normalized backend status, primal solution status and backend message. The exitflag distinguishes optimal, infeasible, unbounded, limit-reached and early-stop statuses when the backend provides that status.

Options such as MaxTime, MaxNodes, MaxIterations, MaxFeasiblePoints, AbsoluteGapTolerance, RelativeGapTolerance, IntegerTolerance, LPPreprocess, RootLPAlgorithm, Heuristics and CutGeneration are mapped to HiGHS where possible. Recognized options without a direct backend equivalent are accepted and ignored.

💡Examples

f = [8; 1];
intcon = 2;
A = [-1 -2; -4 -1; 2 1];
b = [14; -33; 20];
opts = optimoptions('intlinprog', 'Display', 'off');
[x, fval, exitflag, output] = intlinprog(f, intcon, A, b, [], [], [], [], [], opts)

🔗See Also

linprog optimoptions prob2struct

Used Functions

optimoptions prob2struct

📚Bibliography

Huangfu, Q. and Hall, J. A. J., Parallelizing the dual revised simplex method, Mathematical Programming Computation, 2018. Achterberg, T., Constraint Integer Programming, PhD thesis, Technische Universitaet Berlin, 2007. Nemhauser, G. L. and Wolsey, L. A., Integer and Combinatorial Optimization, Wiley, 1988.