linprog(method=’simplex’)¶

scipy.optimize.
linprog
(c, A_ub=None, b_ub=None, A_eq=None, b_eq=None, bounds=None, method='simplex', callback=None, options={'maxiter': 5000, 'disp': False, 'presolve': True, 'tol': 1e12, 'autoscale': False, 'rr': True, 'bland': False}, x0=None) Linear programming: minimize a linear objective function subject to linear equality and inequality constraints using the tablueabased simplex method.
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
andub = None
unless specified withbounds
. Parameters
 c1D array
The coefficients of the linear objective function to be minimized.
 A_ub2D array, optional
The inequality constraint matrix. Each row of
A_ub
specifies the coefficients of a linear inequality constraint onx
. b_ub1D array, optional
The inequality constraint vector. Each element represents an upper bound on the corresponding value of
A_ub @ x
. A_eq2D array, optional
The equality constraint matrix. Each row of
A_eq
specifies the coefficients of a linear equality constraint onx
. b_eq1D array, optional
The equality constraint vector. Each element of
A_eq @ x
must equal the corresponding element ofb_eq
. boundssequence, optional
A sequence of
(min, max)
pairs for each element inx
, defining the minimum and maximum values of that decision variable. UseNone
to indicate that there is no bound. By default, bounds are(0, None)
(all decision variables are nonnegative). If a single tuple(min, max)
is provided, thenmin
andmax
will serve as bounds for all decision variables. methodstr
This is the methodspecific documentation for ‘simplex’. ‘highs’, ‘highsds’, ‘highsipm’, ‘interiorpoint’ (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: x1D 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
. slack1D array
The (nominally positive) values of the slack variables,
b_ub  A_ub @ x
. con1D 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.
See also
For documentation for the rest of the parameters, see
scipy.optimize.linprog
 Options
 maxiterint (default: 5000)
The maximum number of iterations to perform in either phase.
 dispbool (default: False)
Set to
True
if indicators of optimization status are to be printed to the console each iteration. presolvebool (default: True)
Presolve attempts to identify trivial infeasibilities, identify trivial unboundedness, and simplify the problem before sending it to the main solver. It is generally recommended to keep the default setting
True
; set toFalse
if presolve is to be disabled. tolfloat (default: 1e12)
The tolerance which determines when a solution is “close enough” to zero in Phase 1 to be considered a basic feasible solution or close enough to positive to serve as an optimal solution.
 autoscalebool (default: False)
Set to
True
to automatically perform equilibration. Consider using this option if the numerical values in the constraints are separated by several orders of magnitude. rrbool (default: True)
Set to
False
to disable automatic redundancy removal. blandbool
If True, use Bland’s anticycling rule [3] to choose pivots to prevent cycling. If False, choose pivots which should lead to a converged solution more quickly. The latter method is subject to cycling (nonconvergence) in rare instances.
 unknown_optionsdict
Optional arguments not used by this particular solver. If unknown_options is nonempty a warning is issued listing all unused options.
References
 1
Dantzig, George B., Linear programming and extensions. Rand Corporation Research Study Princeton Univ. Press, Princeton, NJ, 1963
 2
Hillier, S.H. and Lieberman, G.J. (1995), “Introduction to Mathematical Programming”, McGrawHill, Chapter 4.
 3
Bland, Robert G. New finite pivoting rules for the simplex method. Mathematics of Operations Research (2), 1977: pp. 103107.