linprog(method=’highs-ipm’)#
- 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 HiGHS interior point solver. - 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 = 0and- ub = Noneunless 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_ubspecifies 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_eqspecifies the coefficients of a linear equality constraint on- x.
- b_eq1-D array, optional
- The equality constraint vector. Each element of - A_eq @ xmust 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- Noneto 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- minand- maxwill serve as bounds for all decision variables.
- methodstr
- This is the method-specific documentation for ‘highs-ipm’. ‘highs-ipm’, ‘highs-ds’, ‘interior-point’ (default), ‘revised simplex’, and ‘simplex’ (legacy) are also available. 
 
- Returns:
- resOptimizeResult
- A - scipy.optimize.OptimizeResultconsisting 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, - b_ub - A_ub @ x.
- con1D array
- The (nominally zero) residuals of the equality constraints, - b_eq - A_eq @ x.
- successbool
- Truewhen the algorithm succeeds in finding an optimal solution.
- statusint
- 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.
- messagestr
- A string descriptor of the exit status of the algorithm. 
- nitint
- The total number of iterations performed. For the HiGHS interior-point method, this does not include crossover iterations. 
- crossover_nitint
- The number of primal/dual pushes performed during the crossover routine for the HiGHS interior-point method. 
- ineqlinOptimizeResult
- Solution and sensitivity information corresponding to the inequality constraints, b_ub. A dictionary consisting of the fields: - residualnp.ndnarray
- The (nominally positive) values of the slack variables, - b_ub - A_ub @ x. This quantity is also commonly referred to as “slack”.
- marginalsnp.ndarray
- The sensitivity (partial derivative) of the objective function with respect to the right-hand side of the inequality constraints, b_ub. 
 
- eqlinOptimizeResult
- Solution and sensitivity information corresponding to the equality constraints, b_eq. A dictionary consisting of the fields: - residualnp.ndarray
- The (nominally zero) residuals of the equality constraints, - b_eq - A_eq @ x.
- marginalsnp.ndarray
- The sensitivity (partial derivative) of the objective function with respect to the right-hand side of the equality constraints, b_eq. 
 
- lower, upperOptimizeResult
- Solution and sensitivity information corresponding to the lower and upper bounds on decision variables, bounds. - residualnp.ndarray
- The (nominally positive) values of the quantity - x - lb(lower) or- ub - x(upper).
- marginalsnp.ndarray
- The sensitivity (partial derivative) of the objective function with respect to the lower and upper bounds. 
 
 
 
 - See also - For documentation for the rest of the parameters, see - scipy.optimize.linprog- Options:
- ——-
- maxiterint
- The maximum number of iterations to perform in either phase. For ‘highs-ipm’, this does not include the number of crossover iterations. Default is the largest possible value for an - inton the platform.
- dispbool (default: False)
- Set to - Trueif indicators of optimization status are to be printed to the console during optimization.
- 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 to- Falseif presolve is to be disabled.
- time_limitfloat
- The maximum time in seconds allotted to solve the problem; default is the largest possible value for a - doubleon the platform.
- dual_feasibility_tolerancedouble (default: 1e-07)
- The minimum of this and - primal_feasibility_toleranceis used for the feasibility tolerance of ‘highs-ipm’.
- primal_feasibility_tolerancedouble (default: 1e-07)
- The minimum of this and - dual_feasibility_toleranceis used for the feasibility tolerance of ‘highs-ipm’.
- ipm_optimality_tolerancedouble (default: 1e-08)
- Optimality tolerance for ‘highs-ipm’. Minimum allowable value is 1e-12. 
- unknown_optionsdict
- Optional arguments not used by this particular solver. If - unknown_optionsis non-empty, a warning is issued listing all unused options.
 
 - Notes - Method ‘highs-ipm’ is a wrapper of a C++ implementation of an interior-point method [13]; it features a crossover routine, so it is as accurate as a simplex solver. Method ‘highs-ds’ is a wrapper of the C++ high performance dual revised simplex implementation (HSOL) [13], [14]. Method ‘highs’ chooses between the two automatically. For new code involving - linprog, we recommend explicitly choosing one of these three method values instead of ‘interior-point’ (default), ‘revised simplex’, and ‘simplex’ (legacy).- 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 [13] (1,2)- Huangfu, Q., Galabova, I., Feldmeier, M., and Hall, J. A. J. “HiGHS - high performance software for linear optimization.” https://highs.dev/ [14]- 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