to be minimized.
    `c` is converted to a double precision array before the problem is
    solved.
integrality : 1D dense array_like, optional
    Indicates the type of integrality constraint on each decision variable.

    ``0`` : Continuous variable; no integrality constraint.

    ``1`` : Integer variable; decision variable must be an integer
    within `bounds`.

    ``2`` : Semi-continuous variable; decision variable must be within
    `bounds` or take value ``0``.

    ``3`` : Semi-integer variable; decision variable must be an integer
    within `bounds` or take value ``0``.

    By default, all variables are continuous. `integrality` is converted
    to an array of integers before the problem is solved.

bounds : scipy.optimize.Bounds, optional
    Bounds on the decision variables. Lower and upper bounds are converted
    to double precision arrays before the problem is solved. The
    ``keep_feasible`` parameter of the `Bounds` object is ignored. If
    not specified, all decision variables are constrained to be
    non-negative.
constraints : sequence of scipy.optimize.LinearConstraint, optional
    Linear constraints of the optimization problem. Arguments may be
    one of the following:

    1. A single `LinearConstraint` object
    2. A single tuple that can be converted to a `LinearConstraint` object
       as ``LinearConstraint(*constraints)``
    3. A sequence composed entirely of objects of type 1. and 2.

    Before the problem is solved, all values are converted to double
    precision, and the matrices of constraint coefficients are converted to
    instances of `scipy.sparse.csc_array`. The ``keep_feasible`` parameter
    of `LinearConstraint` objects is ignored.
options : dict, optional
    A dictionary of solver options. The following keys are recognized.

    disp : bool (default: ``False``)
        Set to ``True`` if indicators of optimization status are to be
        printed to the console during optimization.
    node_limit : int, optional
        The maximum number of nodes (linear program relaxations) to solve
        before stopping. Default is no maximum number of nodes.
    presolve : bool (default: ``True``)
        Presolve attempts to identify trivial infeasibilities,
        identify trivial unboundedness, and simplify the problem before
        sending it to the main solver.
    time_limit : float, optional
        The maximum number of seconds allotted to solve the problem.
        Default is no time limit.
    mip_rel_gap : float, optional
        Termination criterion for MIP solver: solver will terminate when
        the gap between the primal objective value and the dual objective
        bound, scaled by the primal objective value, is <= mip_rel_gap.

Returns
-------
res : OptimizeResult
    An instance of :class:`scipy.optimize.OptimizeResult`. The object
    is guaranteed to have the following attributes.

    status : int
        An integer representing the exit status of the algorithm.

        ``0`` : Optimal solution found.

        ``1`` : Iteration or time limit reached.

        ``2`` : Problem is infeasible.

        ``3`` : Problem is unbounded.

        ``4`` : Other; see message for details.

    success : bool
        ``True`` when an optimal solution is found and ``False`` otherwise.

    message : str
        A string descriptor of the exit status of the algorithm.

    The following attributes will also be present, but the values may be
    ``None``, depending on the solution status.

    x : ndarray
        The values of the decision variables that minimize the
        objective function while satisfying the constraints.
    fun : float
        The optimal value of the objective function ``c @ x``.
    mip_node_count : int
        The number of subproblems or "nodes" solved by the MILP solver.
    mip_dual_bound : float
        The MILP solver's final estimate of the lower bound on the optimal
        solution.
    mip_gap : float
        The difference between the primal objective value and the dual
        objective bound, scaled by the primal objective value.

Notes
-----
`milp` is a wrapper of the HiGHS linear optimization software [1]_. The
algorithm is deterministic, and it typically finds the global optimum of
moderately challenging mixed-integer linear programs (when it exists).

References
----------
.. [1] Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J.
       "HiGHS - high performance software for linear optimization."
       https://highs.dev/
.. [2] Huangfu, Q. and Hall, J. A. J. "Parallelizing the dual revised
       simplex method." Mathematical Programming Computation, 10 (1),
       119-142, 2018. DOI: 10.1007/s12532-017-0130-5

Examples
--------
Consider the problem at
https://en.wikipedia.org/wiki/Integer_programming#Example, which is
expressed as a maximization problem of two variables. Since `milp` requires
that the problem be expressed as a minimization problem, the objective
function coefficients on the decision variables are:

>>> import numpy as np
>>> c = -np.array([0, 1])

Note the negative sign: we maximize the original objective function
by minimizing the negative of the objective function.

We collect the coefficients of the constraints into arrays like:

>>> A = np.array([[-1, 1], [3, 2], [2, 3]])
>>> b_u = np.array([1, 12, 12])
>>> b_l = np.full_like(b_u, -np.inf, dtype=float)

Because there is no lower limit on these constraints, we have defined a
variable ``b_l`` full of values representing negative infinity. This may
be unfamiliar to users of `scipy.optimize.linprog`, which only accepts
"less than" (or "upper bound") inequality constraints of the form
``A_ub @ x <= b_u``. By accepting both ``b_l`` and ``b_u`` of constraints
``b_l <= A_ub @ x <= b_u``, `milp` makes it easy to specify "greater than"
inequality constraints, "less than" inequality constraints, and equality
constraints concisely.

These arrays are collected into a single `LinearConstraint` object like:

>>> from scipy.optimize import LinearConstraint
>>> constraints = LinearConstraint(A, b_l, b_u)

The non-negativity bounds on the decision variables are enforced by
default, so we do not need to provide an argument for `bounds`.

Finally, the problem states that both decision variables must be integers:

>>> integrality = np.ones_like(c)

We solve the problem like:

>>> from scipy.optimize import milp
>>> res = milp(c=c, constraints=constraints, integrality=integrality)
>>> res.x
[2.0, 2.0]

Note that had we solved the relaxed problem (without integrality
constraints):

>>> res = milp(c=c, constraints=constraints)  # OR:
>>> # from scipy.optimize import linprog; res = linprog(c, A, b_u)
>>> res.x
[1.8, 2.8]

we would not have obtained the correct solution by rounding to the nearest
integers.

Other examples are given :ref:`in the tutorial <tutorial-optimize_milp>`.

