o ֭j@sddlZddlZddlmZmZmZmZddlm Z ddl m Z m Z m Z mZmZddlmZmZmZmZmZddlmZmZmZmZmZmZ     dd d Zd d Zd dZddZ ddZ!ddZ"ddZ#ddZ$dS)N)BoundsLinearConstraintNonlinearConstraintOptimizeResult) TrustRegion)ObjectiveFunctionBoundConstraintsLinearConstraintsNonlinearConstraintsProblem) MaxEvalError TargetSuccessCallbackSuccessFeasibleSuccessexact_1d_array) ExitStatusOptions ConstantsDEFAULT_OPTIONSDEFAULT_CONSTANTS PRINT_OPTIONSc3 Ks |duri}nt|}|tjttj}t|}|tjttj} t| } |tjttj} t| } |tj ttj } t| } tj |vrS|tj dkrSt d|tj ttj } t | } tj |vrq|tj dkrqt d|tj ttj } t | } |tjttj}t|}t|ts|f}t|||g|R}t|ds|g}t|}tt||}t|\}}t|||}t|||}t||||||| | | | | | }t||jtdi|}|jjst|ddt j!d|S|jdkrt|ddt j"d|S|r3t#d t#d |tj$d t#d |tj%d t#d |tj&d t#d|tj'd t#zt(|||}Wnbt)yOt|ddt j*d|YSt+ybt|ddt j,d|YSt-yut|ddt j.d|YSt/yt|ddt j0d|YSt1j2j3yt|ddt j4d|YSwd}d}d}d}d}d} ||tj'krt j0}nJ|d7}t1j25|j6|j7j8j9|t:j;|j<kr|=||j<}|>|\} }!| |!}"t1j25|"}#|#|t:j?|j@krY|j<|t:jA9_<||j@kr d}d}n|d7}|d7}|#d|j@krd}|dkp$|dk}$|$r0d}d}d}%nz|B\}}&Wnt1j2j3yHt j4}Ynw|&tC|j<|t:jD|j@k}%n|E|"}'|'r;z tF|||"|\}(})}*Wn;t)y}t j*}d}Ynt-yt j.}d}Ynvt+yt j,}d}Yngt/yt jG}YnZw|H|j6|jI|jJ|jK}+|H|j6|"|(|)|*},|jLdkr7|,|+kr7t1j25| |t:jMd|j<kr7|N|"|}-t1j25|-dkr7|"|-7}"z tF|||"|\}(})}*Wn;t)y t j*}d}Ynt-yt j.}d}Ynt+y)t j,}d}Ynt/y6t jG}Ynw|O|"|(|)|*}.z |B|j6|"d}Wnt1j2j3y[t j4}Ynwz|j7P||j6|"|(|)|*}/Wnt1j2j3y{t j4}Ynw|Q|R|"|.|j<|j@kr|.|t:jSkrd}nX|d7}|j7T|j6}0z |j7U|j6}1Wnt1j2j3yt j4}YnFwt1j25|0|t:jVt1j25|1krd}|dkrz|j7WWnt1j2j3yt j4}Ynwd}|X|j6|"z|B\}}&Wnt1j2j3yt j4}Ynw|/p(|.|t:jYko(|&tC|j<|t:jD|j@k}%||j@ko9|.|t:jYko9|% }$nd}$d}%|$r~|j@|tj%krQd}t jZ}n|[||\|r~|]|j6|jJ|jK}2t^d|j@||_|j6|jI|2|j`|t#|%rz|a||}"Wnt1j2j3yt j4}Ynjwz tF|||"|\}(})}*Wn7t)yt j*}d}YnNt-yt j.}d}Yn@t+yt j,}d}Yn2t/yt jG}Yn&wz|j7P||j6|"|(|)|*Wnt1j2j3yt j4}Ynw|Qqt||jb||||S)a? Minimize a scalar function using the COBYQA method. The Constrained Optimization BY Quadratic Approximations (COBYQA) method is a derivative-free optimization method designed to solve general nonlinear optimization problems. A complete description of COBYQA is given in [3]_. Parameters ---------- fun : {callable, None} Objective function to be minimized. ``fun(x, *args) -> float`` where ``x`` is an array with shape (n,) and `args` is a tuple. If `fun` is ``None``, the objective function is assumed to be the zero function, resulting in a feasibility problem. x0 : array_like, shape (n,) Initial guess. args : tuple, optional Extra arguments passed to the objective function. bounds : {`scipy.optimize.Bounds`, array_like, shape (n, 2)}, optional Bound constraints of the problem. It can be one of the cases below. #. An instance of `scipy.optimize.Bounds`. For the time being, the argument ``keep_feasible`` is disregarded, and all the constraints are considered unrelaxable and will be enforced. #. An array with shape (n, 2). The bound constraints for ``x[i]`` are ``bounds[i][0] <= x[i] <= bounds[i][1]``. Set ``bounds[i][0]`` to :math:`-\infty` if there is no lower bound, and set ``bounds[i][1]`` to :math:`\infty` if there is no upper bound. The COBYQA method always respect the bound constraints. constraints : {Constraint, list}, optional General constraints of the problem. It can be one of the cases below. #. An instance of `scipy.optimize.LinearConstraint`. The argument ``keep_feasible`` is disregarded. #. An instance of `scipy.optimize.NonlinearConstraint`. The arguments ``jac``, ``hess``, ``keep_feasible``, ``finite_diff_rel_step``, and ``finite_diff_jac_sparsity`` are disregarded. #. A list, each of whose elements are described in the cases above. callback : callable, optional A callback executed at each objective function evaluation. The method terminates if a ``StopIteration`` exception is raised by the callback function. Its signature can be one of the following: ``callback(intermediate_result)`` where ``intermediate_result`` is a keyword parameter that contains an instance of `scipy.optimize.OptimizeResult`, with attributes ``x`` and ``fun``, being the point at which the objective function is evaluated and the value of the objective function, respectively. The name of the parameter must be ``intermediate_result`` for the callback to be passed an instance of `scipy.optimize.OptimizeResult`. Alternatively, the callback function can have the signature: ``callback(xk)`` where ``xk`` is the point at which the objective function is evaluated. Introspection is used to determine which of the signatures to invoke. options : dict, optional Options passed to the solver. Accepted keys are: disp : bool, optional Whether to print information about the optimization procedure. Default is ``False``. maxfev : int, optional Maximum number of function evaluations. Default is ``500 * n``. maxiter : int, optional Maximum number of iterations. Default is ``1000 * n``. target : float, optional Target on the objective function value. The optimization procedure is terminated when the objective function value of a feasible point is less than or equal to this target. Default is ``-numpy.inf``. feasibility_tol : float, optional Tolerance on the constraint violation. If the maximum constraint violation at a point is less than or equal to this tolerance, the point is considered feasible. Default is ``numpy.sqrt(numpy.finfo(float).eps)``. radius_init : float, optional Initial trust-region radius. Typically, this value should be in the order of one tenth of the greatest expected change to `x0`. Default is ``1.0``. radius_final : float, optional Final trust-region radius. It should indicate the accuracy required in the final values of the variables. Default is ``1e-6``. nb_points : int, optional Number of interpolation points used to build the quadratic models of the objective and constraint functions. Default is ``2 * n + 1``. scale : bool, optional Whether to scale the variables according to the bounds. Default is ``False``. filter_size : int, optional Maximum number of points in the filter. The filter is used to select the best point returned by the optimization procedure. Default is ``sys.maxsize``. store_history : bool, optional Whether to store the history of the function evaluations. Default is ``False``. history_size : int, optional Maximum number of function evaluations to store in the history. Default is ``sys.maxsize``. debug : bool, optional Whether to perform additional checks during the optimization procedure. This option should be used only for debugging purposes and is highly discouraged to general users. Default is ``False``. Other constants (from the keyword arguments) are described below. They are not intended to be changed by general users. They should only be changed by users with a deep understanding of the algorithm, who want to experiment with different settings. Returns ------- `scipy.optimize.OptimizeResult` Result of the optimization procedure, with the following fields: message : str Description of the cause of the termination. success : bool Whether the optimization procedure terminated successfully. status : int Termination status of the optimization procedure. x : `numpy.ndarray`, shape (n,) Solution point. fun : float Objective function value at the solution point. maxcv : float Maximum constraint violation at the solution point. nfev : int Number of function evaluations. nit : int Number of iterations. If ``store_history`` is True, the result also has the following fields: fun_history : `numpy.ndarray`, shape (nfev,) History of the objective function values. maxcv_history : `numpy.ndarray`, shape (nfev,) History of the maximum constraint violations. A description of the termination statuses is given below. .. list-table:: :widths: 25 75 :header-rows: 1 * - Exit status - Description * - 0 - The lower bound for the trust-region radius has been reached. * - 1 - The target objective function value has been reached. * - 2 - All variables are fixed by the bound constraints. * - 3 - The callback requested to stop the optimization procedure. * - 4 - The feasibility problem received has been solved successfully. * - 5 - The maximum number of function evaluations has been exceeded. * - 6 - The maximum number of iterations has been exceeded. * - -1 - The bound constraints are infeasible. * - -2 - A linear algebra error occurred. Other Parameters ---------------- decrease_radius_factor : float, optional Factor by which the trust-region radius is reduced when the reduction ratio is low or negative. Default is ``0.5``. increase_radius_factor : float, optional Factor by which the trust-region radius is increased when the reduction ratio is large. Default is ``numpy.sqrt(2.0)``. increase_radius_threshold : float, optional Threshold that controls the increase of the trust-region radius when the reduction ratio is large. Default is ``2.0``. decrease_radius_threshold : float, optional Threshold used to determine whether the trust-region radius should be reduced to the resolution. Default is ``1.4``. decrease_resolution_factor : float, optional Factor by which the resolution is reduced when the current value is far from its final value. Default is ``0.1``. large_resolution_threshold : float, optional Threshold used to determine whether the resolution is far from its final value. Default is ``250.0``. moderate_resolution_threshold : float, optional Threshold used to determine whether the resolution is close to its final value. Default is ``16.0``. low_ratio : float, optional Threshold used to determine whether the reduction ratio is low. Default is ``0.1``. high_ratio : float, optional Threshold used to determine whether the reduction ratio is high. Default is ``0.7``. very_low_ratio : float, optional Threshold used to determine whether the reduction ratio is very low. This is used to determine whether the models should be reset. Default is ``0.01``. penalty_increase_threshold : float, optional Threshold used to determine whether the penalty parameter should be increased. Default is ``1.5``. penalty_increase_factor : float, optional Factor by which the penalty parameter is increased. Default is ``2.0``. short_step_threshold : float, optional Factor used to determine whether the trial step is too short. Default is ``0.5``. low_radius_factor : float, optional Factor used to determine which interpolation point should be removed from the interpolation set at each iteration. Default is ``0.1``. byrd_omojokun_factor : float, optional Factor by which the trust-region radius is reduced for the computations of the normal step in the Byrd-Omojokun composite-step approach. Default is ``0.8``. threshold_ratio_constraints : float, optional Threshold used to determine which constraints should be taken into account when decreasing the penalty parameter. Default is ``2.0``. large_shift_factor : float, optional Factor used to determine whether the point around which the quadratic models are built should be updated. Default is ``10.0``. large_gradient_factor : float, optional Factor used to determine whether the models should be reset. Default is ``10.0``. resolution_factor : float, optional Factor by which the resolution is decreased. Default is ``2.0``. improve_tcg : bool, optional Whether to improve the steps computed by the truncated conjugate gradient method when the trust-region boundary is reached. Default is ``True``. References ---------- .. [1] J. Nocedal and S. J. Wright. *Numerical Optimization*. Springer Ser. Oper. Res. Financ. Eng. Springer, New York, NY, USA, second edition, 2006. `doi:10.1007/978-0-387-40065-5 `_. .. [2] M. J. D. Powell. A direct search optimization method that models the objective and constraint functions by linear interpolation. In S. Gomez and J.-P. Hennart, editors, *Advances in Optimization and Numerical Analysis*, volume 275 of Math. Appl., pages 51--67. Springer, Dordrecht, Netherlands, 1994. `doi:10.1007/978-94-015-8330-5_4 `_. .. [3] T. M. Ragonneau. *Model-Based Derivative-Free Optimization Methods and Software*. PhD thesis, Department of Applied Mathematics, The Hong Kong Polytechnic University, Hong Kong, China, 2022. URL: https://theses.lib.polyu.edu.hk/handle/200/12294. Examples -------- To demonstrate how to use `minimize`, we first minimize the Rosenbrock function implemented in `scipy.optimize` in an unconstrained setting. .. testsetup:: import numpy as np np.set_printoptions(precision=3, suppress=True) >>> from cobyqa import minimize >>> from scipy.optimize import rosen To solve the problem using COBYQA, run: >>> x0 = [1.3, 0.7, 0.8, 1.9, 1.2] >>> res = minimize(rosen, x0) >>> res.x array([1., 1., 1., 1., 1.]) To see how bound and constraints are handled using `minimize`, we solve Example 16.4 of [1]_, defined as .. math:: \begin{aligned} \min_{x \in \mathbb{R}^2} & \quad (x_1 - 1)^2 + (x_2 - 2.5)^2\\ \text{s.t.} & \quad -x_1 + 2x_2 \le 2,\\ & \quad x_1 + 2x_2 \le 6,\\ & \quad x_1 - 2x_2 \le 2,\\ & \quad x_1 \ge 0,\\ & \quad x_2 \ge 0. \end{aligned} >>> import numpy as np >>> from scipy.optimize import Bounds, LinearConstraint Its objective function can be implemented as: >>> def fun(x): ... return (x[0] - 1.0)**2 + (x[1] - 2.5)**2 This problem can be solved using `minimize` as: >>> x0 = [2.0, 0.0] >>> bounds = Bounds([0.0, 0.0], np.inf) >>> constraints = LinearConstraint([ ... [-1.0, 2.0], ... [1.0, 2.0], ... [1.0, -2.0], ... ], -np.inf, [2.0, 6.0, 2.0]) >>> res = minimize(fun, x0, bounds=bounds, constraints=constraints) >>> res.x array([1.4, 1.7]) To see how nonlinear constraints are handled, we solve Problem (F) of [2]_, defined as .. math:: \begin{aligned} \min_{x \in \mathbb{R}^2} & \quad -x_1 - x_2\\ \text{s.t.} & \quad x_1^2 - x_2 \le 0,\\ & \quad x_1^2 + x_2^2 \le 1. \end{aligned} >>> from scipy.optimize import NonlinearConstraint Its objective and constraint functions can be implemented as: >>> def fun(x): ... return -x[0] - x[1] >>> >>> def cub(x): ... return [x[0]**2 - x[1], x[0]**2 + x[1]**2] This problem can be solved using `minimize` as: >>> x0 = [1.0, 1.0] >>> constraints = NonlinearConstraint(cub, -np.inf, [0.0, 1.0]) >>> res = minimize(fun, x0, constraints=constraints) >>> res.x array([0.707, 0.707]) Finally, to see how to supply linear and nonlinear constraints simultaneously, we solve Problem (G) of [2]_, defined as .. math:: \begin{aligned} \min_{x \in \mathbb{R}^3} & \quad x_3\\ \text{s.t.} & \quad 5x_1 - x_2 + x_3 \ge 0,\\ & \quad -5x_1 - x_2 + x_3 \ge 0,\\ & \quad x_1^2 + x_2^2 + 4x_2 \le x_3. \end{aligned} Its objective and nonlinear constraint functions can be implemented as: >>> def fun(x): ... return x[2] >>> >>> def cub(x): ... return x[0]**2 + x[1]**2 + 4.0*x[1] - x[2] This problem can be solved using `minimize` as: >>> x0 = [1.0, 1.0, 1.0] >>> constraints = [ ... LinearConstraint( ... [[5.0, -1.0, 1.0], [-5.0, -1.0, 1.0]], ... [0.0, 0.0], ... np.inf, ... ), ... NonlinearConstraint(cub, -np.inf, 0.0), ... ] >>> res = minimize(fun, x0, constraints=constraints) >>> res.x array([ 0., -3., -3.]) Nrz)The size of the history must be positive.z(The size of the filter must be positive.__len__FTz$Starting the optimization procedure.zInitial trust-region radius: .zFinal trust-region radius: z(Maximum number of function evaluations: zMaximum number of iterations: rg?znonlinearly constrained@zNew trust-region radius: r)cdictgetrVERBOSErboolFEASIBILITY_TOLfloatSCALE STORE_HISTORY HISTORY_SIZE ValueErrorint FILTER_SIZEDEBUG isinstancetuplerhasattrlenr _get_bounds_get_constraintsr r r _set_default_optionsn_set_default_constantsbounds is_feasible _build_resultrINFEASIBLE_ERROR FIXED_SUCCESSprintRHOBEGRHOENDMAX_EVALMAX_ITERrrTARGET_SUCCESSrCALLBACK_SUCCESSrFEASIBLE_SUCCESSr MAX_ITER_WARNINGnplinalg LinAlgError LINALG_ERRORnormx_bestmodels interpolationx_baserLARGE_SHIFT_FACTORradius shift_x_baseget_trust_region_stepSHORT_STEP_THRESHOLD resolutionDECREASE_RESOLUTION_FACTORget_index_to_removemaxRESOLUTION_FACTORincrease_penalty_evalMAX_EVAL_WARNINGmeritfun_bestcub_bestceq_besttypeBYRD_OMOJOKUN_FACTOR get_second_order_correction_stepget_reduction_ratioupdate_interpolationset_best_index update_radiusVERY_LOW_RATIOfun_grad fun_alt_gradLARGE_GRADIENT_FACTOR reset_modelsset_multipliers LOW_RATIORADIUS_SUCCESSenhance_resolutiondecrease_penaltymaxcv _print_stepbuild_xn_evalget_geometry_steppenalty)3funx0argsr5 constraintscallbackoptionskwargsverbosefeasibility_tolscale store_history history_size filter_sizedebugobjn_origlinear_constraintsnonlinear_constraintslinear nonlinearpb constants frameworksuccessn_iterk_new n_short_stepsn_very_short_steps n_alt_modelsstatus radius_save normal_steptangential_stepsteps_normrlimprove_geometrydist_newsame_best_pointfun_valcub_valceq_val merit_old merit_newsoc_stepratioill_conditionedgradgrad_alt maxcv_valrrS/var/www/html/CropPilot/venv/lib/python3.10/site-packages/scipy/_lib/cobyqa/main.pyminimize$s0                            rcCs|durtt|tj t|tjSt|tr6|jj|fks'|jj|fkr/td|dt|j|jSt |dr\t |}|j|dfkrKtdt|dddf|dddfSt d ) z Uniformize the bounds. NzThe bounds must have z elements.rzGThe shape of the bounds is not compatible with the number of variables.rrzPThe bounds must be an instance of scipy.optimize.Bounds or an array-like object.) rrCfullinfr,lbshapeubr(r.asarray TypeError)r5r3rrrr0qs     "r0c Cs(t|ts t|ds |f}g}g}|D]|}t|tr7t|jd}t|jd}|t|jgt ||Rqt|t rYt|jd}t|jd}|t |j gt ||Rqt|trd|vsh|ddvrlt dd |vsvt|d szt d ||d |d|d d d qtd||fS)z7 Extract the linear and nonlinear constraints. rz;The lower bound of the linear constraints must be a vector.z;The upper bound of the linear constraints must be a vector.z>The lower bound of the nonlinear constraints must be a vector.z>The upper bound of the nonlinear constraints must be a vector.r])eqineqz+The constraint type must be "eq" or "ineq".rtz)The constraint function must be callable.rvr)rtr]rvzrThe constraints must be instances of scipy.optimize.LinearConstraint, scipy.optimize.NonlinearConstraint, or dict.)r,rr.rrrrappendArCbroadcast_arraysrrtr(callabler r)rwrr constraintrrrrrr1sh      r1cCstj|vr|tjdkrtdtj|vr |tjdkr tdtj|vr9tj|vr9|tj|tjkr8tdn@tj|vrPtttj|tjg|tjj<n)tj|vrgtttj|tjg|tjj<nttj|tjj<ttj|tjj<t |tj|tjj<t |tj|tjj<tj |vr|tj dkrtdtj |vr|tj |d|ddkrtd |d|ddd | tj jttj |t |tj |tj j<tj |vr|tj dkrtd | tj jtttj ||tj dgt |tj |tj j<tj|vr|tjdkrtd | tjjttj|t |tj|tjj<| tjjttjt |tj|tjj<| tjjttjt |tj|tjj<| tjjttjt|tj|tjj<| tjjttjt|tj|tjj<| tjjttjt |tj|tjj<| tjjttjt|tj|tjj<| tjjttjt |tj|tjj<| tjjttjt|tj|tjj<|D]}|tjvrtd |d tdqdS)z" Set the default options. rz1The initial trust-region radius must be positive.z2The final trust-region radius must be nonnegative.z_The initial trust-region radius must be greater than or equal to the final trust-region radius.rz4The number of interpolation points must be positive.rrz3The number of interpolation points must be at most rzTARGETr#r!r"r%r*r&r'r+ __members__valueswarningswarnRuntimeWarning)ryr3keyrrrr2s        r2cKst|}|tjjttjt|tj|tjj<|tjdks(|tjdkr,td|tjjttjt|tj|tjj<|tjdkrMtdtj |vr]|tj dkr]tdtj |vrm|tj dkrmtdtj |vrtj |vr|tj |tj krtdnFtj |vrt ttj dd|tj g|tj j<n+tj |vrt ttj d |tj g|tj j<nttj |tj j<ttj |tj j<|tjjttjt|tj|tjj<|tjdks|tjdkrtd tj|vr|tjdkrtd tj|vr|tjdkrtd tj|vr4tj|vr4|tj|tjkr3td nBtj|vrLt ttj|tjg|tjj<n*tj|vrdt ttj|tjg|tjj<nttj|tjj<ttj|tjj<tj|vr|tjdks|tjdkrtdtj|vr|tjdks|tjdkrtdtj|vrtj|vr|tj|tjkrtdnBtj|vrt ttj|tjg|tjj<n*tj|vrt ttj|tjg|tjj<nttj|tjj<ttj|tjj<|tjjttjt|tj|tjj<|tjdks.|tjdkr2tdtj|vrD|tjdkrDtdtj|vrV|tjdkrVtdtj|vrrtj|vrr|tj|tjkrqtdnBtj|vrt ttj|tjg|tjj<n*tj|vrt ttj|tjg|tjj<nttj|tjj<ttj|tjj<|tjjttjt|tj|tjj<|tjdks|tjdkrtd|tjjttjt|tj|tjj<|tjdks|tjdkrtd|tjjttjt|tj|tjj<|tjdks.|tjdkr2td|tjjttjt|tj|tjj<|tjdkrTtd|tjjttjt|tj|tjj<|tjdkrvtd|tjjttjt|tj|tjj<|tjdkrtd|tjjttjt|tj|tjj<|tjdkrtd|tjjttjt|tj|tjj<|D]}|tj vrt!"d|dt#dq|S)z$ Set the default constants. rg?zCThe constant decrease_radius_factor must be in the interval (0, 1).z>The constant increase_radius_threshold must be greater than 1.z;The constant increase_radius_factor must be greater than 1.z>The constant decrease_radius_threshold must be greater than 1.zPThe constant decrease_radius_threshold must be less than increase_radius_factor.g?rzGThe constant decrease_resolution_factor must be in the interval (0, 1).z?The constant large_resolution_threshold must be greater than 1.zBThe constant moderate_resolution_threshold must be greater than 1.zVThe constant moderate_resolution_threshold must be at most large_resolution_threshold.z6The constant low_ratio must be in the interval (0, 1).z7The constant high_ratio must be in the interval (0, 1).z2The constant low_ratio must be at most high_ratio.z;The constant very_low_ratio must be in the interval (0, 1).zKThe constant penalty_increase_threshold must be greater than or equal to 1.zThe constant low_radius_factor must be in the interval (0, 1).zAThe constant byrd_omojokun_factor must be in the interval (0, 1).z@The constant threshold_ratio_constraints must be greater than 1.z4The constant large_shift_factor must be nonnegative.z:The constant large_gradient_factor must be greater than 1.z6The constant resolution_factor must be greater than 1.zUnknown constant: rr)$rrrDECREASE_RADIUS_FACTORrrr$r(INCREASE_RADIUS_THRESHOLDINCREASE_RADIUS_FACTORDECREASE_RADIUS_THRESHOLDrCrrTrRLARGE_RESOLUTION_THRESHOLDMODERATE_RESOLUTION_THRESHOLDrj HIGH_RATIOrdPENALTY_INCREASE_THRESHOLDPENALTY_INCREASE_FACTORrPLOW_RADIUS_FACTORr^THRESHOLD_RATIO_CONSTRAINTSrLrgrU IMPROVE_TCGr"rrrrr)rzrrrrrr47s2                                          r4c Cs|j|tjkr t|j|}|||j\}}}||||}||tjkr/||tjkr/t |j r;||tjkr;t |||fS)z: Evaluate the objective and constraint functions. ) rqrr=r rHrsrnrr#ris_feasibilityr) rrrryx_evalrrrr_valrrrrWs  rWc Cs||\}}}|ot|ot|}|tjtjfvr%|o$||tjk}t} tj dtjdtj dtj dtjdtj dtj dtjdtjd i |d | _|| _|j| _||| _|| _|| _|j| _|| _|tjrq|j| _|j| _|tjrt | j|| j| j| j| j| j| S) z7 Build the result of the optimization process. zs8    SEhY 5