+ /iBRt^RIt^RIt^RIHtHt^RIHt^RI H t ^RI H t H t HtHtHt^RIHtHtHtRtRtR tR R ltR#) a^HiGHS Linear Optimization Methods Interface to HiGHS linear optimization software. https://highs.dev/ .. versionadded:: 1.5.0 References ---------- .. [1] Q. Huangfu and J.A.J. Hall. "Parallelizing the dual revised simplex method." Mathematical Programming Computation, 10 (1), 119-142, 2018. DOI: 10.1007/s12532-017-0130-5 N)OptimizeWarningOptimizeResult)warn)_highs_wrapper) kHighsInfHighsDebugLevelObjSenseHighsModelStatussimplex_constants) csc_arrayvstackissparsecr/RRb\PRb\PRb\PRb\PRb\P Rb\P Rb\PRb\PRb\PRb\PRb\PR b\PR b\PR b\PR b\PR bpRpVP!W4wrEVe \#V4MRpV RV RV R2pWE3#)zCConverts HiGHS status number/message to SciPy status number/messageNz(HiGHS Status z: ))z%HiGHS did not provide a status code. )r)r)z&Optimization terminated successfully. )zTime limit reached. )rzIteration limit reached. )rzThe problem is infeasible. )zThe problem is unbounded. )rz(The problem is unbounded or infeasible. )rz*The HiGHS status code was not recognized. )r kNotset kLoadError kModelErrorkPresolveError kSolveErrorkPostsolveError kModelEmptykObjectiveBoundkObjectiveTargetkOptimal kTimeLimitkIterationLimit kInfeasible kUnboundedkUnboundedOrInfeasiblegetint) highs_status highs_messagescipy_statuses_messages unrecognized scipy_status scipy_messagehstats&& [/var/www/html/photoedit/myenv/lib/python3.14/site-packages/scipy/optimize/_linprog_highs.py_highs_to_scipy_status_messager/"sF :F  'F ##WF $$g F '' F $$g F (('F $$gF (('F ))7F !!#PF ##%@F ((*JF $$&HF ##%FF //2E!F$EL##L? 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Using default: . stacklevel) lowerAttributeErrorKeyErrorinspect signature_linprog_highs parametersdefaultrsetkeysr)option option_strchoicessig default_strs&&& r._convert_to_highs_enumrOHs $||~&&  $/nnZ088  wzl$vh.CGLLN#$$A}A ,##$sB/B/A6B/.B/c   V 'dRV R2p \V \^R7\V RR\PP R\PP R\PPR\PPR R /R 7pVwppppppppVPP4wpp\P!R R 7;_uu_4\P!V4)\P,pR R R 4TpTpTp\P!XV34p\P!VV34p\!V4'g\!V4'd\#VV34pM\P"!VV34p\%V4p/R VbR\&P(bRVbRVbR\*P,bRVbRVbRVbRV bRVbRVbRVbR\P.P0bRVbRVbRV bp V P3V 4\5V4p\5V4p\5V4p\5V4pVe\P6!V4^8Xd\P8!^4pM\P:!V4p\=VVP>VP@VPBVVVVVPE\PF4V 4 p!RV!9dOV!R,p"\P:!V"\IV4R 4p#\P:!V"R \IV44p"MR R p#p"RV!9dV!R,p$\P:!V$R \IV44p%\P:!V$\IV4R 4p&\P:!V!R,R3,4p'\P:!V!R,R4,4p(MR R p&p%R R p(p'V!PKRR 4p)V!PKR R 4p*\MV)V*4wp+p V!R!,p,R!T,RT"R"T#R#\OR$V"R%V%/4R&\OR$V#R%V&/4R'\OR$V,fR MV,V, R%V(/4R(\OR$V,fR MVV,, R%V'/4R)V!PKR)4RT+R*V!R,\PPR8HR T R+V!PKR,^4;'gV!PKR-^4R.V!PKR.4/ p-\PT!V,4'dLVeHV-P3R/V!PKR/^4R0V!PKR0R14R2V!PKR2R14/4V-# +'giELE;i)5a Solve the following linear programming problem using one of the HiGHS solvers: User-facing documentation is in _linprog_doc.py. Parameters ---------- lp : _LPProblem A ``scipy.optimize._linprog_util._LPProblem`` ``namedtuple``. solver : "ipm" or "simplex" or None Which HiGHS solver to use. If ``None``, "simplex" will be used. Options ------- maxiter : int The maximum number of iterations to perform in either phase. For ``solver='ipm'``, this does not include the number of crossover iterations. Default is the largest possible value for an ``int`` on the platform. disp : bool Set to ``True`` if indicators of optimization status are to be printed to the console each iteration; default ``False``. time_limit : float The maximum time in seconds allotted to solve the problem; default is the largest possible value for a ``double`` on the platform. presolve : bool 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. dual_feasibility_tolerance : double Dual feasibility tolerance. Default is 1e-07. The minimum of this and ``primal_feasibility_tolerance`` is used for the feasibility tolerance when ``solver='ipm'``. primal_feasibility_tolerance : double Primal feasibility tolerance. Default is 1e-07. The minimum of this and ``dual_feasibility_tolerance`` is used for the feasibility tolerance when ``solver='ipm'``. ipm_optimality_tolerance : double Optimality tolerance for ``solver='ipm'``. Default is 1e-08. Minimum possible value is 1e-12 and must be smaller than the largest possible value for a ``double`` on the platform. simplex_dual_edge_weight_strategy : str (default: None) Strategy for simplex dual edge weights. The default, ``None``, automatically selects one of the following. ``'dantzig'`` uses Dantzig's original strategy of choosing the most negative reduced cost. ``'devex'`` uses the strategy described in [15]_. ``steepest`` uses the exact steepest edge strategy as described in [16]_. ``'steepest-devex'`` begins with the exact steepest edge strategy until the computation is too costly or inexact and then switches to the devex method. Currently, using ``None`` always selects ``'steepest-devex'``, but this may change as new options become available. mip_max_nodes : int The maximum number of nodes allotted to solve the problem; default is the largest possible value for a ``HighsInt`` on the platform. Ignored if not using the MIP solver. 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 ------- sol : dict A dictionary consisting of the fields: x : 1D 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 : 1D array The (nominally positive) values of the slack, ``b_ub - A_ub @ x``. con : 1D 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 or time limit reached. ``2`` : Problem appears to be infeasible. ``3`` : Problem appears to be unbounded. ``4`` : The HiGHS solver ran into a problem. message : str A string descriptor of the exit status of the algorithm. nit : int The total number of iterations performed. For ``solver='simplex'``, this includes iterations in all phases. For ``solver='ipm'``, this does not include crossover iterations. crossover_nit : int The number of primal/dual pushes performed during the crossover routine for ``solver='ipm'``. This is ``0`` for ``solver='simplex'``. ineqlin : OptimizeResult Solution and sensitivity information corresponding to the inequality constraints, `b_ub`. A dictionary consisting of the fields: residual : np.ndnarray The (nominally positive) values of the slack variables, ``b_ub - A_ub @ x``. This quantity is also commonly referred to as "slack". marginals : np.ndarray The sensitivity (partial derivative) of the objective function with respect to the right-hand side of the inequality constraints, `b_ub`. eqlin : OptimizeResult Solution and sensitivity information corresponding to the equality constraints, `b_eq`. A dictionary consisting of the fields: residual : np.ndarray The (nominally zero) residuals of the equality constraints, ``b_eq - A_eq @ x``. marginals : np.ndarray The sensitivity (partial derivative) of the objective function with respect to the right-hand side of the equality constraints, `b_eq`. lower, upper : OptimizeResult Solution and sensitivity information corresponding to the lower and upper bounds on decision variables, `bounds`. residual : np.ndarray The (nominally positive) values of the quantity ``x - lb`` (lower) or ``ub - x`` (upper). marginals : np.ndarray The sensitivity (partial derivative) of the objective function with respect to the lower and upper `bounds`. mip_node_count : int The number of subproblems or "nodes" solved by the MILP solver. Only present when `integrality` is not `None`. mip_dual_bound : float The MILP solver's final estimate of the lower bound on the optimal solution. Only present when `integrality` is not `None`. mip_gap : float The difference between the final objective function value and the final dual bound, scaled by the final objective function value. Only present when `integrality` is not `None`. Notes ----- The result fields `ineqlin`, `eqlin`, `lower`, and `upper` all contain `marginals`, or partial derivatives of the objective function with respect to the right-hand side of each constraint. These partial derivatives are also referred to as "Lagrange multipliers", "dual values", and "shadow prices". The sign convention of `marginals` is opposite that of Lagrange multipliers produced by many nonlinear solvers. References ---------- .. [15] Harris, Paula MJ. "Pivot selection methods of the Devex LP code." Mathematical programming 5.1 (1973): 1-28. .. [16] Goldfarb, Donald, and John Ker Reid. "A practicable steepest-edge simplex algorithm." Mathematical Programming 12.1 (1977): 361-371. zUnrecognized options detected: z). 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