linprog(method=’simplex’)#

scipy.optimize.linprog(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=(0, None), method='highs', callback=None, options=None, x0=None, integrality=None)

Linear programming: minimize a linear objective function subject to linear equality and inequality constraints using the tableau-based simplex method.

Deprecated since version 1.9.0: method=’simplex’ will be removed in SciPy 1.11.0. It is replaced by method=’highs’ because the latter is faster and more robust.

Linear programming solves problems of the following form:

\[\begin{split}\min_x \ & c^T x \\ \mbox{such that} \ & A_{ub} x \leq b_{ub},\\ & A_{eq} x = b_{eq},\\ & l \leq x \leq u ,\end{split}\]

where \(x\) is a vector of decision variables; \(c\), \(b_{ub}\), \(b_{eq}\), \(l\), and \(u\) are vectors; and \(A_{ub}\) and \(A_{eq}\) are matrices.

Alternatively, that’s:

minimize:

c @ x

such that:

A_ub @ x <= b_ub
A_eq @ x == b_eq
lb <= x <= ub

Note that by default lb = 0 and ub = None unless specified with bounds.

Parameters:

c1-D array: The coefficients of the linear objective function to be minimized.
A_ub2-D array, optional: The inequality constraint matrix. Each row of A_ub specifies the coefficients of a linear inequality constraint on x.
b_ub1-D array, optional: The inequality constraint vector. Each element represents an upper bound on the corresponding value of A_ub @ x.
A_eq2-D array, optional: The equality constraint matrix. Each row of A_eq specifies the coefficients of a linear equality constraint on x.
b_eq1-D array, optional: The equality constraint vector. Each element of A_eq @ x must equal the corresponding element of b_eq.
boundssequence, optional: A sequence of (min, max) pairs for each element in x, defining the minimum and maximum values of that decision variable. Use None to indicate that there is no bound. By default, bounds are (0, None) (all decision variables are non-negative). If a single tuple (min, max) is provided, then min and max will serve as bounds for all decision variables.
methodstr: This is the method-specific documentation for ‘simplex’. ‘highs’, ‘highs-ds’, ‘highs-ipm’, ‘interior-point’ (default), and ‘revised simplex’ are also available.
callbackcallable, optional: Callback function to be executed once per iteration.

Returns:

resOptimizeResult

A scipy.optimize.OptimizeResult consisting of the fields:

x1-D array

The values of the decision variables that minimizes the objective function while satisfying the constraints.

funfloat

The optimal value of the objective function c @ x.

slack1-D array

The (nominally positive) values of the slack variables, b_ub - A_ub @ x.

con1-D array

The (nominally zero) residuals of the equality constraints, b_eq - A_eq @ x.

successbool

True when the algorithm succeeds in finding an optimal solution.

statusint

An integer representing the exit status of the algorithm.

0 : Optimization terminated successfully.

1 : Iteration limit reached.

2 : Problem appears to be infeasible.

3 : Problem appears to be unbounded.

4 : Numerical difficulties encountered.

messagestr

A string descriptor of the exit status of the algorithm.

nitint

The total number of iterations performed in all phases.