scipy.optimize._trustregion_constr.minimize_trustregion_constr:_minimize_trustregion_constr

Parameters

gtol : float, optional

Tolerance for termination by the norm of the Lagrangian gradient. The algorithm will terminate when both the infinity norm (i.e., max abs value) of the Lagrangian gradient and the constraint violation are smaller than gtol. Default is 1e-8.

xtol : float, optional

Tolerance for termination by the change of the independent variable. The algorithm will terminate when tr_radius < xtol, where tr_radius is the radius of the trust region used in the algorithm. Default is 1e-8.

barrier_tol : float, optional

Threshold on the barrier parameter for the algorithm termination. When inequality constraints are present, the algorithm will terminate only when the barrier parameter is less than barrier_tol. Default is 1e-8.

sparse_jacobian : {bool, None}, optional

Determines how to represent Jacobians of the constraints. If bool, then Jacobians of all the constraints will be converted to the corresponding format. If None (default), then Jacobians won't be converted, but the algorithm can proceed only if they all have the same format.

initial_tr_radius: float, optional

Initial trust radius. The trust radius gives the maximum distance between solution points in consecutive iterations. It reflects the trust the algorithm puts in the local approximation of the optimization problem. For an accurate local approximation the trust-region should be large and for an approximation valid only close to the current point it should be a small one. The trust radius is automatically updated throughout the optimization process, with initial_tr_radius being its initial value. Default is 1 (recommended in ^[1], p. 19).

initial_constr_penalty : float, optional

Initial constraints penalty parameter. The penalty parameter is used for balancing the requirements of decreasing the objective function and satisfying the constraints. It is used for defining the merit function: merit_function(x) = fun(x) + constr_penalty * constr_norm_l2(x), where constr_norm_l2(x) is the l2 norm of a vector containing all the constraints. The merit function is used for accepting or rejecting trial points and constr_penalty weights the two conflicting goals of reducing objective function and constraints. The penalty is automatically updated throughout the optimization process, with initial_constr_penalty being its initial value. Default is 1 (recommended in ^[1], p 19).

initial_barrier_parameter, initial_barrier_tolerance: float, optional

Initial barrier parameter and initial tolerance for the barrier subproblem. Both are used only when inequality constraints are present. For dealing with optimization problems min_x f(x) subject to inequality constraints c(x) <= 0 the algorithm introduces slack variables, solving the problem min_(x,s) f(x) + barrier_parameter*sum(ln(s)) subject to the equality constraints c(x) + s = 0 instead of the original problem. This subproblem is solved for decreasing values of barrier_parameter and with decreasing tolerances for the termination, starting with initial_barrier_parameter for the barrier parameter and initial_barrier_tolerance for the barrier tolerance. Default is 0.1 for both values (recommended in ^[1] p. 19). Also note that barrier_parameter and barrier_tolerance are updated with the same prefactor.

factorization_method : string or None, optional

Method to factorize the Jacobian of the constraints. Use None (default) for the auto selection or one of:

• 'NormalEquation' (requires scikit-sparse)

• 'AugmentedSystem'

• 'QRFactorization'

• 'SVDFactorization'

The methods 'NormalEquation' and 'AugmentedSystem' can be used only with sparse constraints. The projections required by the algorithm will be computed using, respectively, the normal equation and the augmented system approaches explained in ^[1]. 'NormalEquation' computes the Cholesky factorization of A A.T and 'AugmentedSystem' performs the LU factorization of an augmented system. They usually provide similar results. 'AugmentedSystem' is used by default for sparse matrices.

The methods 'QRFactorization' and 'SVDFactorization' can be used only with dense constraints. They compute the required projections using, respectively, QR and SVD factorizations. The 'SVDFactorization' method can cope with Jacobian matrices with deficient row rank and will be used whenever other factorization methods fail (which may imply the conversion of sparse matrices to a dense format when required). By default, 'QRFactorization' is used for dense matrices.

finite_diff_rel_step : None or array_like, optional

Relative step size for the finite difference approximation.

maxiter : int, optional

Maximum number of algorithm iterations. Default is 1000.

verbose : {0, 1, 2, 3}, optional

Level of algorithm's verbosity:

• 0 (default)work silently.

• 1display a termination report.

• 2display progress during iterations.

• 3display progress during iterations (more complete report).

disp : bool, optional

If True (default), then verbose will be set to 1 if it was 0.

workers : int, map-like callable, optional

A map-like callable, such as multiprocessing.Pool.map for evaluating any numerical differentiation in parallel. This evaluation is carried out as workers(fun, iterable).