:ref:`'highs' `, :ref:`'highs-ds' `, :ref:`'highs-ipm' `, :ref:`'interior-point' ` (default), and :ref:`'simplex' ` (legacy) are also available. callback : callable, optional Callback function to be executed once per iteration. x0 : 1-D array, optional Guess values of the decision variables, which will be refined by the optimization algorithm. This argument is currently used only by the 'revised simplex' method, and can only be used if `x0` represents a basic feasible solution. Options ------- maxiter : int (default: 5000) The maximum number of iterations to perform in either phase. disp : bool (default: False) Set to ``True`` if indicators of optimization status are to be printed to the console each iteration. presolve : bool (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 to ``False`` if presolve is to be disabled. tol : float (default: 1e-12) 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. autoscale : bool (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. rr : bool (default: True) Set to ``False`` to disable automatic redundancy removal. maxupdate : int (default: 10) The maximum number of updates performed on the LU factorization. After this many updates is reached, the basis matrix is factorized from scratch. mast : bool (default: False) Minimize Amortized Solve Time. If enabled, the average time to solve a linear system using the basis factorization is measured. Typically, the average solve time will decrease with each successive solve after initial factorization, as factorization takes much more time than the solve operation (and updates). Eventually, however, the updated factorization becomes sufficiently complex that the average solve time begins to increase. When this is detected, the basis is refactorized from scratch. Enable this option to maximize speed at the risk of nondeterministic behavior. Ignored if ``maxupdate`` is 0. pivot : "mrc" or "bland" (default: "mrc") Pivot rule: Minimum Reduced Cost ("mrc") or Bland's rule ("bland"). Choose Bland's rule if iteration limit is reached and cycling is suspected. unknown_options : dict Optional arguments not used by this particular solver. If `unknown_options` is non-empty a warning is issued listing all unused options. Returns ------- res : OptimizeResult A :class:`scipy.optimize.OptimizeResult` consisting of the fields: x : 1-D array The values of the decision variables that minimizes the objective function while satisfying the constraints. fun : float The optimal value of the objective function ``c @ x``. slack : 1-D array The (nominally positive) values of the slack variables, ``b_ub - A_ub @ x``. con : 1-D array The (nominally zero) residuals of the equality constraints, ``b_eq - A_eq @ x``. success : bool ``True`` when the algorithm succeeds in finding an optimal solution. status : int 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. ``5`` : Problem has no constraints; turn presolve on. ``6`` : Invalid guess provided. message : str A string descriptor of the exit status of the algorithm. nit : int The total number of iterations performed in all phases. Notes ----- Method *revised simplex* uses the revised simplex method as described in [9]_, except that a factorization [11]_ of the basis matrix, rather than its inverse, is efficiently maintained and used to solve the linear systems at each iteration of the algorithm. References ---------- .. [9] Bertsimas, Dimitris, and J. Tsitsiklis. "Introduction to linear programming." Athena Scientific 1 (1997): 997. .. [11] Bartels, Richard H. "A stabilization of the simplex method." Journal in Numerische Mathematik 16.5 (1971): 414-434. Nr