CasADi Interface

For most purposes, it is recommended to use the the high-level problem API to compose optimization problems using CasADi. However, in some cases, you may want access to the alpaqa─CasADi interface directly. This lower-level interface is documented here.

alpaqa.casadi_generator.generate_casadi_problem(f: Function, g: Function | None, second_order: Literal['no', 'full', 'prod', 'L', 'L_prod', 'psi', 'psi_prod']='no', name: str = 'alpaqa_problem', sym: Callable = <function GenSX.sym>) → CodeGenerator

Convert the objective and constraint functions into a CasADi code generator.

Parameters:

• f – Objective function.

• g – Constraint function.

• second_order – Whether to generate functions for evaluating Hessians.

• name – Optional string description of the problem (used for filename).

• sym – Symbolic variable constructor, usually either casadi.SX.sym (default) or casadi.MX.sym.

Returns:

Code generator that generates the functions and derivatives used by the solvers.

alpaqa.casadi_generator.generate_casadi_control_problem(f: Function, l: Function, l_N: Function, h: Function | None = None, h_N: Function | None = None, c: Function | None = None, c_N: Function | None = None, name: str = 'alpaqa_control_problem') → CodeGenerator

Convert the dynamics and cost functions into a CasADi code generator.

Parameters:

• f – Dynamics.

• name – Optional string description of the problem (used for filename).

Returns:

Code generator that generates the functions and derivatives used by the solvers.

alpaqa.casadi_generator.write_casadi_problem_data(sofile, C, D, param, l1_reg, penalty_alm_split, name)

Write the CSV file with constant data for the problem.

alpaqa.casadi_generator.write_casadi_control_problem_data(sofile, U, D, D_N, x_init, param, penalty_alm_split=0, penalty_alm_split_N=None)

Write the CSV file with constant data for the problem.

alpaqa.casadi_loader.generate_and_compile_casadi_problem_no_load(f: Function, g: Function, *, C=None, D=None, param=None, l1_reg=None, penalty_alm_split=None, second_order: Literal['no', 'full', 'prod', 'L', 'L_prod', 'psi', 'psi_prod'] = 'no', name: str = 'alpaqa_problem', **kwargs) → Path

Compile the objective and constraint functions into a alpaqa Problem.

Parameters:

• f – Objective function f(x).

• g – Constraint function g(x).

• C – Bound constraints on x.

• D – Bound constraints on g(x).

• param – Problem parameter values.

• l1_reg – L1-regularization on x.

• penalty_alm_split – This many components at the beginning of g(x) are handled using a quadratic penalty method rather than an augmented Lagrangian method.

• second_order – Whether to generate functions for evaluating Hessians.

• name – Optional string description of the problem (used for filename).

• kwargs – Parameters passed to casadi_generator.generate_casadi_problem().

Returns:

Path to the shared object file with CasADi functions that can be loaded by the solvers.

Note

If you copy the shared object file, don’t forget to also copy the accompanying CSV file with problem data.

alpaqa.casadi_loader.generate_and_compile_casadi_problem(*args, **kwargs) → CasADiProblem

Calls generate_and_compile_casadi_problem_no_load() and loads the resulting problem file.

Returns:

Problem specification that can be passed to the solvers.

alpaqa.load_casadi_problem(so_name: str) → alpaqa._alpaqa.float64.CasADiProblem

Load a compiled CasADi problem.

class alpaqa.CasADiProblem

C++ documentation: alpaqa::CasADiProblem

See alpaqa.Problem for the full documentation.

__init__(self: alpaqa._alpaqa.float64.CasADiProblem, other: alpaqa._alpaqa.float64.CasADiProblem) → None

Create a copy

check(self: alpaqa._alpaqa.float64.CasADiProblem) → None

eval_augmented_lagrangian(*args, **kwargs)

Overloaded function.

1. eval_augmented_lagrangian(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]], ŷ: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> float

2. eval_augmented_lagrangian(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]]) -> tuple[float, numpy.ndarray[numpy.float64[m, 1]]]

eval_augmented_lagrangian_and_gradient(*args, **kwargs)

Overloaded function.

1. eval_augmented_lagrangian_and_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1], flags.writeable], work_n: numpy.ndarray[numpy.float64[m, 1], flags.writeable], work_m: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> float

2. eval_augmented_lagrangian_and_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]]) -> tuple[float, numpy.ndarray[numpy.float64[m, 1]]]

eval_augmented_lagrangian_gradient(*args, **kwargs)

Overloaded function.

1. eval_augmented_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1], flags.writeable], work_n: numpy.ndarray[numpy.float64[m, 1], flags.writeable], work_m: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_augmented_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_augmented_lagrangian_hessian(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]], scale: float = 1.0) → tuple[object, alpaqa._alpaqa.Symmetry]

Returns the Hessian of the augmented Lagrangian and its symmetry.

eval_augmented_lagrangian_hessian_product(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], Σ: numpy.ndarray[numpy.float64[m, 1]], scale: float, v: numpy.ndarray[numpy.float64[m, 1]], Hv: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → None

eval_constraints(*args, **kwargs)

Overloaded function.

1. eval_constraints(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], gx: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_constraints(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_constraints_gradient_product(*args, **kwargs)

Overloaded function.

1. eval_constraints_gradient_product(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], grad_gxy: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_constraints_gradient_product(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_constraints_jacobian(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]]) → tuple[object, alpaqa._alpaqa.Symmetry]

Returns the Jacobian of the constraints and its symmetry.

eval_grad_gi(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], i: int, grad_gi: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → None

eval_inactive_indices_res_lna(*args, **kwargs)

Overloaded function.

1. eval_inactive_indices_res_lna(self: alpaqa._alpaqa.float64.CasADiProblem, γ: float, x: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1]], J: numpy.ndarray[numpy.int64[m, 1], flags.writeable]) -> int

2. eval_inactive_indices_res_lna(self: alpaqa._alpaqa.float64.CasADiProblem, γ: float, x: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.int64[m, 1]]

eval_lagrangian_gradient(*args, **kwargs)

Overloaded function.

1. eval_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], grad_L: numpy.ndarray[numpy.float64[m, 1], flags.writeable], work_n: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_lagrangian_hessian(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], scale: float = 1.0) → tuple[object, alpaqa._alpaqa.Symmetry]

Returns the Hessian of the Lagrangian and its symmetry.

eval_lagrangian_hessian_product(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]], scale: float, v: numpy.ndarray[numpy.float64[m, 1]], Hv: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → None

eval_objective(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]]) → float

eval_objective_and_gradient(*args, **kwargs)

Overloaded function.

1. eval_objective_and_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], grad_fx: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> float

2. eval_objective_and_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]]) -> tuple

eval_objective_gradient(*args, **kwargs)

Overloaded function.

1. eval_objective_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]], grad_fx: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_objective_gradient(self: alpaqa._alpaqa.float64.CasADiProblem, x: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_projecting_difference_constraints(*args, **kwargs)

Overloaded function.

1. eval_projecting_difference_constraints(self: alpaqa._alpaqa.float64.CasADiProblem, z: numpy.ndarray[numpy.float64[m, 1]], e: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> None

2. eval_projecting_difference_constraints(self: alpaqa._alpaqa.float64.CasADiProblem, z: numpy.ndarray[numpy.float64[m, 1]]) -> numpy.ndarray[numpy.float64[m, 1]]

eval_projection_multipliers(self: alpaqa._alpaqa.float64.CasADiProblem, y: numpy.ndarray[numpy.float64[m, 1], flags.writeable], M: float) → None

eval_proximal_gradient_step(*args, **kwargs)

Overloaded function.

1. eval_proximal_gradient_step(self: alpaqa._alpaqa.float64.CasADiProblem, γ: float, x: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1]], x_hat: numpy.ndarray[numpy.float64[m, 1], flags.writeable], p: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) -> float

2. eval_proximal_gradient_step(self: alpaqa._alpaqa.float64.CasADiProblem, γ: float, x: numpy.ndarray[numpy.float64[m, 1]], grad_ψ: numpy.ndarray[numpy.float64[m, 1]]) -> tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], float]

get_general_bounds(self: alpaqa._alpaqa.float64.CasADiProblem) → alpaqa._alpaqa.float64.Box

get_variable_bounds(self: alpaqa._alpaqa.float64.CasADiProblem) → alpaqa._alpaqa.float64.Box

property num_constraints

Number of general constraints, dimension of \(g(x)\)

property num_variables

Number of decision variables, dimension of \(x\)

property param

Parameter vector \(p\) of the problem

provides_eval_augmented_lagrangian(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_augmented_lagrangian_and_gradient(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_augmented_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_augmented_lagrangian_hessian(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_augmented_lagrangian_hessian_product(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_constraints_jacobian(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_grad_gi(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_lagrangian_gradient(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_lagrangian_hessian(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_eval_lagrangian_hessian_product(self: alpaqa._alpaqa.float64.CasADiProblem) → bool

provides_get_variable_bounds(self: alpaqa._alpaqa.float64.CasADiProblem) → bool