Python API Reference¶

Inner PANOC solver¶

class alpaqa._alpaqa.PANOCSolver

C++ documentation: pa::PANOCSolver

__call__(self: alpaqa._alpaqa.PANOCSolver, problem: alpaqa._alpaqa.Problem, Σ: numpy.ndarray[numpy.float64[m, 1]], ε: float, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) → Tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], dict]

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.PANOCSolver) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], lbfgs_direction: alpaqa._alpaqa.LBFGSDirection) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], lbfgs_params: Union[alpaqa._alpaqa.LBFGSParams, dict]) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], direction: alpaqa._alpaqa.PANOCDirection) -> None

set_progress_callback(self: alpaqa._alpaqa.PANOCSolver, callback: Callable[[alpaqa._alpaqa.PANOCProgressInfo], None]) → None: Attach a callback that is called on each iteration of the solver.

property direction

property params

class alpaqa._alpaqa.PANOCParams

C++ documentation: pa::PANOCParams

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.PANOCParams) -> None
__init__(self: alpaqa._alpaqa.PANOCParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.PANOCParams) → dict

property L_max

property L_min

property Lipschitz

property alternative_linesearch_cond

property lbfgs_stepsize

property max_iter

property max_no_progress

property max_time

property print_interval

property quadratic_upperbound_tolerance_factor

property update_lipschitz_in_linesearch

property τ_min

class alpaqa._alpaqa.LBFGSParams

C++ documentation: pa::LBFGSParams

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.LBFGSParams) -> None
__init__(self: alpaqa._alpaqa.LBFGSParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.LBFGSParams) → dict

property cbfgs

property memory

property rescale_when_γ_changes

Inner Structured PANOC solver¶

class alpaqa._alpaqa.StructuredPANOCLBFGSSolver

C++ documentation: pa::StructuredPANOCLBFGSSolver

__call__(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver, problem: alpaqa._alpaqa.Problem, Σ: numpy.ndarray[numpy.float64[m, 1]], ε: float, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) → Tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], dict]

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None
__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver, panoc_params: Union[alpaqa._alpaqa.StructuredPANOCLBFGSParams, dict], lbfgs_params: Union[alpaqa._alpaqa.LBFGSParams, dict]) -> None

set_progress_callback(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver, callback: Callable[[alpaqa._alpaqa.StructuredPANOCLBFGSProgressInfo], None]) → None: Attach a callback that is called on each iteration of the solver.

property params

class alpaqa._alpaqa.StructuredPANOCLBFGSParams

C++ documentation: pa::StructuredPANOCLBFGSParams

__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSParams, **kwargs) → None

to_dict(self: alpaqa._alpaqa.StructuredPANOCLBFGSParams) → dict

property L_max

property L_min

property Lipschitz

property alternative_linesearch_cond

property full_augmented_hessian

property hessian_step_size_heuristic

property hessian_vec

property hessian_vec_finite_differences

property lbfgs_stepsize

property max_iter

property max_no_progress

property max_time

property nonmonotone_linesearch

property print_interval

property quadratic_upperbound_tolerance_factor

property stop_crit

property update_lipschitz_in_linesearch

property τ_min

Outer ALM solver¶

class alpaqa._alpaqa.ALMSolver

Main augmented Lagrangian solver.

C++ documentation: pa::ALMSolver

__call__(self: alpaqa._alpaqa.ALMSolver, problem: alpaqa._alpaqa.Problem, x: Optional[numpy.ndarray[numpy.float64[m, 1]]] = None, y: Optional[numpy.ndarray[numpy.float64[m, 1]]] = None) → Tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], dict]

Solve.

Parameters

problem – Problem to solve.
y – Initial guess for Lagrange multipliers \(y\)
x – Initial guess for decision variables \(x\)

Returns

Lagrange multipliers \(y\) at the solution
Solution \(x\)
Statistics

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.ALMSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], panoc_solver: alpaqa._alpaqa.PANOCSolver) -> None

Build an ALM solver using PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], pga_solver: alpaqa._alpaqa.PGASolver) -> None

Build an ALM solver using the projected gradient algorithm as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], structuredpanoc_solver: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], inner_solver: alpaqa._alpaqa.InnerSolver) -> None

Build an ALM solver using a custom inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, panoc_solver: alpaqa._alpaqa.PANOCSolver) -> None

Build an ALM solver using PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, pga_solver: alpaqa._alpaqa.PGASolver) -> None

Build an ALM solver using the projected gradient algorithm as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, structuredpanoc_solver: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, inner_solver: alpaqa._alpaqa.InnerSolver) -> None

Build an ALM solver using a custom inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: alpaqa._alpaqa.ALMParams) -> None

Build an ALM solver using Structured PANOC as inner solver.

property inner_solver

property params

class alpaqa._alpaqa.ALMParams

C++ documentation: pa::ALMParams

__init__(*args, **kwargs)

Overloaded function.

__init__(self: alpaqa._alpaqa.ALMParams) -> None
__init__(self: alpaqa._alpaqa.ALMParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.ALMParams) → dict

property M

property max_iter

property max_num_initial_retries

property max_num_retries

property max_time

property max_total_num_retries

property preconditioning

property print_interval

property single_penalty_factor

property Δ

property Δ_lower

property Σ_0

property Σ_0_lower

property Σ_max

property Σ_min

property δ

property ε

property ε_0

property ε_0_increase

property θ

property ρ

property ρ_increase

property σ_0

Problem formulation¶

class alpaqa._alpaqa.Problem

C++ documentation: pa::Problem

__init__(self: alpaqa._alpaqa.Problem, n: int, m: int) → None

Parameters

n – Number of unknowns
m – Number of constraints

property C: Box constraints on \(x\)

property D: Box constraints on \(g(x)\)

property f: Objective funcion, \(f(x)\)

property g: Constraint function, \(g(x)\)

property grad_f: Gradient of the objective function, \(\nabla f(x)\)

property grad_g_prod: Gradient of constraint function times vector, \(\nabla g(x)\, v\)

property grad_gi: Gradient vector of the \(i\)-th component of the constriant function, \(\nabla g_i(x)\)

property hess_L: Hessian of the Lagrangian function, \(\nabla^2_{xx} L(x,y)\)

property hess_L_prod: Hessian of the Lagrangian function times vector, \(\nabla^2_{xx} L(x,y)\, v\)

property m: Number of general constraints, dimension of \(g(x)\)

property n: Number of unknowns, dimension of \(x\)

class alpaqa._alpaqa.ProblemWithParam

C++ documentation: pa::ProblemWithParam

See alpaqa._alpaqa.Problem for the full documentation.

__init__(*args, **kwargs)

property C

property D

property f

property g

property grad_f

property grad_g_prod

property grad_gi

property hess_L

property hess_L_prod

property m

property n

property param: Parameter vector \(p\) of the problem

CasADi Interface¶

alpaqa.casadi_problem.generate_and_compile_casadi_problem(f: casadi.casadi.Function, g: casadi.casadi.Function, second_order: bool = False, name: str = 'PANOC_ALM_problem') → Union[alpaqa._alpaqa.Problem, alpaqa._alpaqa.ProblemWithParam][source]

Compile the objective and constraint functions into a alpaqa Problem.

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).

Returns

Problem specification that can be passed to the solvers.

alpaqa.casadi_problem.generate_casadi_problem(f: casadi.casadi.Function, g: casadi.casadi.Function, second_order: bool = False, name: str = 'PANOC_ALM_problem') → Tuple[casadi.casadi.CodeGenerator, int, int, int][source]

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).

Returns

Code generator that generates the functions and derivatives used by the solvers.
Dimensions of the decision variables (primal dimension).
Number of nonlinear constraints (dual dimension).
Number of parameters.

All¶

PANOC+ALM solvers

class alpaqa._alpaqa.ALMParams¶

C++ documentation: pa::ALMParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.ALMParams) -> None
__init__(self: alpaqa._alpaqa.ALMParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.ALMParams) → dict¶

property M¶

property max_iter¶

property max_num_initial_retries¶

property max_num_retries¶

property max_time¶

property max_total_num_retries¶

property preconditioning¶

property print_interval¶

property single_penalty_factor¶

property Δ¶

property Δ_lower¶

property Σ_0¶

property Σ_0_lower¶

property Σ_max¶

property Σ_min¶

property δ¶

property ε¶

property ε_0¶

property ε_0_increase¶

property θ¶

property ρ¶

property ρ_increase¶

property σ_0¶

class alpaqa._alpaqa.ALMSolver¶

Main augmented Lagrangian solver.

C++ documentation: pa::ALMSolver

Solve.

Parameters

problem – Problem to solve.
y – Initial guess for Lagrange multipliers \(y\)
x – Initial guess for decision variables \(x\)

Returns

Lagrange multipliers \(y\) at the solution
Solution \(x\)
Statistics

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.ALMSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], panoc_solver: alpaqa._alpaqa.PANOCSolver) -> None

Build an ALM solver using PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], pga_solver: alpaqa._alpaqa.PGASolver) -> None

Build an ALM solver using the projected gradient algorithm as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], structuredpanoc_solver: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: Union[alpaqa._alpaqa.ALMParams, dict], inner_solver: alpaqa._alpaqa.InnerSolver) -> None

Build an ALM solver using a custom inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, panoc_solver: alpaqa._alpaqa.PANOCSolver) -> None

Build an ALM solver using PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, pga_solver: alpaqa._alpaqa.PGASolver) -> None

Build an ALM solver using the projected gradient algorithm as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, structuredpanoc_solver: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None

Build an ALM solver using Structured PANOC as inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, inner_solver: alpaqa._alpaqa.InnerSolver) -> None

Build an ALM solver using a custom inner solver.

__init__(self: alpaqa._alpaqa.ALMSolver, alm_params: alpaqa._alpaqa.ALMParams) -> None

Build an ALM solver using Structured PANOC as inner solver.

property inner_solver¶

property params¶

class alpaqa._alpaqa.Box¶

C++ documentation: pa::Box

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.Box, n: int) -> None

Create an \(n\)-dimensional box at with bounds at \(\pm\infty\) (no constraints).

__init__(self: alpaqa._alpaqa.Box, ub: numpy.ndarray[numpy.float64[m, 1]], lb: numpy.ndarray[numpy.float64[m, 1]]) -> None

Create a box with the given bounds.

property lowerbound¶

property upperbound¶

class alpaqa._alpaqa.EvalCounter¶

C++ documentation: pa::EvalCounter

__init__(*args, **kwargs)¶

property f¶

property g¶

property grad_f¶

property grad_g_prod¶

property grad_gi¶

property hess_L¶

property hess_L_prod¶

property time¶

class alpaqa._alpaqa.EvalTimer¶

C++ documentation: pa::EvalCounter::EvalTimer

__init__(*args, **kwargs)¶

property f¶

property g¶

property grad_f¶

property grad_g_prod¶

property grad_gi¶

property hess_L¶

property hess_L_prod¶

class alpaqa._alpaqa.GAAPGAParams¶

C++ documentation: pa::GAAPGAParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.GAAPGAParams) -> None
__init__(self: alpaqa._alpaqa.GAAPGAParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.GAAPGAParams) → dict¶

property L_max¶

property L_min¶

property Lipschitz¶

property full_flush_on_γ_change¶

property limitedqr_mem¶

property max_iter¶

property max_no_progress¶

property max_time¶

property print_interval¶

property quadratic_upperbound_tolerance_factor¶

property stop_crit¶

class alpaqa._alpaqa.GAAPGAProgressInfo¶

C++ documentation: pa::GAAPGAProgressInfo

__init__(*args, **kwargs)¶

property L¶

property fpr¶

property grad_ψ¶

property grad_ψ_hat¶

property k¶

property norm_sq_p¶

property p¶

property x¶

property x_hat¶

property y¶

property Σ¶

property γ¶

property ε¶

property ψ¶

property ψ_hat¶

class alpaqa._alpaqa.GAAPGASolver¶

C++ documentation: pa::GAAPGASolver

__call__(self: alpaqa._alpaqa.GAAPGASolver, problem: alpaqa._alpaqa.Problem, Σ: numpy.ndarray[numpy.float64[m, 1]], ε: float, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) → Tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], dict]¶

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(self: alpaqa._alpaqa.GAAPGASolver, arg0: alpaqa._alpaqa.GAAPGAParams) → None¶

set_progress_callback(self: alpaqa._alpaqa.GAAPGASolver, callback: Callable[[alpaqa._alpaqa.GAAPGAProgressInfo], None]) → None¶: Attach a callback that is called on each iteration of the solver.

property params¶

class alpaqa._alpaqa.InnerSolver¶

__call__(self: alpaqa._alpaqa.InnerSolver, arg0: alpaqa._alpaqa.Problem, arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: float, arg3: bool, arg4: numpy.ndarray[numpy.float64[m, 1], flags.writeable], arg5: numpy.ndarray[numpy.float64[m, 1], flags.writeable], arg6: numpy.ndarray[numpy.float64[m, 1], flags.writeable]) → alpaqa._alpaqa.InnerSolverStats¶

__init__(self: alpaqa._alpaqa.InnerSolver) → None¶

get_name(self: alpaqa._alpaqa.InnerSolver) → str¶

get_params(self: alpaqa._alpaqa.InnerSolver) → object¶

stop(self: alpaqa._alpaqa.InnerSolver) → None¶

class alpaqa._alpaqa.InnerSolverStats¶

__init__(self: alpaqa._alpaqa.InnerSolverStats, arg0: dict) → None¶

class alpaqa._alpaqa.LBFGSDirection¶

C++ documentation: pa::LBFGSDirection

__init__(self: alpaqa._alpaqa.LBFGSDirection, params: alpaqa._alpaqa.LBFGSParams) → None¶

apply(self: alpaqa._alpaqa.LBFGSDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: float) → numpy.ndarray[numpy.float64[m, 1]]¶

changed_γ(self: alpaqa._alpaqa.LBFGSDirection, arg0: float, arg1: float) → None¶

get_name(self: alpaqa._alpaqa.LBFGSDirection) → str¶

initialize(self: alpaqa._alpaqa.LBFGSDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: numpy.ndarray[numpy.float64[m, 1]]) → None¶

reset(self: alpaqa._alpaqa.LBFGSDirection) → None¶

update(self: alpaqa._alpaqa.LBFGSDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: numpy.ndarray[numpy.float64[m, 1]], arg4: numpy.ndarray[numpy.float64[m, 1]], arg5: alpaqa._alpaqa.Box, arg6: float) → bool¶

property params¶

class alpaqa._alpaqa.LBFGSParams¶

C++ documentation: pa::LBFGSParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.LBFGSParams) -> None
__init__(self: alpaqa._alpaqa.LBFGSParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.LBFGSParams) → dict¶

property cbfgs¶

property memory¶

property rescale_when_γ_changes¶

class alpaqa._alpaqa.LBFGSParamsCBFGS¶

C++ documentation: pa::LBFGSParams::cbfgs

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.LBFGSParamsCBFGS) -> None
__init__(self: alpaqa._alpaqa.LBFGSParamsCBFGS, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.LBFGSParamsCBFGS) → dict¶

property α¶

property ϵ¶

class alpaqa._alpaqa.LBFGSStepsize¶

C++ documentation: pa::LBFGSStepSize

Members:

BasedOnGradientStepSize

BasedOnCurvature

__init__(self: alpaqa._alpaqa.LBFGSStepsize, value: int) → None¶

BasedOnCurvature = <LBFGSStepsize.BasedOnCurvature: 1>¶

BasedOnGradientStepSize = <LBFGSStepsize.BasedOnGradientStepSize: 0>¶

property name¶

property value¶

class alpaqa._alpaqa.LipschitzEstimateParams¶

C++ documentation: pa::LipschitzEstimateParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.LipschitzEstimateParams) -> None
__init__(self: alpaqa._alpaqa.LipschitzEstimateParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.LipschitzEstimateParams) → dict¶

property L_0¶

property Lγ_factor¶

property δ¶

property ε¶

class alpaqa._alpaqa.PANOCDirection¶

Class that provides fast directions for the PANOC algorithm (e.g. L-BFGS)

__init__(self: alpaqa._alpaqa.PANOCDirection) → None¶

apply(self: alpaqa._alpaqa.PANOCDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: float) → numpy.ndarray[numpy.float64[m, 1]]¶

changed_γ(self: alpaqa._alpaqa.PANOCDirection, arg0: float, arg1: float) → None¶

get_name(self: alpaqa._alpaqa.PANOCDirection) → str¶

initialize(self: alpaqa._alpaqa.PANOCDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: numpy.ndarray[numpy.float64[m, 1]]) → None¶

reset(self: alpaqa._alpaqa.PANOCDirection) → None¶

update(self: alpaqa._alpaqa.PANOCDirection, arg0: numpy.ndarray[numpy.float64[m, 1]], arg1: numpy.ndarray[numpy.float64[m, 1]], arg2: numpy.ndarray[numpy.float64[m, 1]], arg3: numpy.ndarray[numpy.float64[m, 1]], arg4: numpy.ndarray[numpy.float64[m, 1]], arg5: alpaqa._alpaqa.Box, arg6: float) → bool¶

class alpaqa._alpaqa.PANOCParams¶

C++ documentation: pa::PANOCParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.PANOCParams) -> None
__init__(self: alpaqa._alpaqa.PANOCParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.PANOCParams) → dict¶

property L_max¶

property L_min¶

property Lipschitz¶

property alternative_linesearch_cond¶

property lbfgs_stepsize¶

property max_iter¶

property max_no_progress¶

property max_time¶

property print_interval¶

property quadratic_upperbound_tolerance_factor¶

property update_lipschitz_in_linesearch¶

property τ_min¶

class alpaqa._alpaqa.PANOCProgressInfo¶

Data passed to the PANOC progress callback.

C++ documentation: pa::PANOCProgressInfo

__init__(*args, **kwargs)¶

property L¶: Estimate of Lipschitz constant of objective \(L\)

property fpr¶: Fixed-point residual \(\left\|p\right\| / \gamma\)

property grad_ψ¶: Gradient of objective \(\nabla\psi(x)\)

property grad_ψ_hat¶

property k¶: Iteration

property norm_sq_p¶: \(\left\|p\right\|^2\)

property p¶: Projected gradient step \(p\)

property x¶: Decision variable \(x\)

property x_hat¶: Decision variable after projected gradient step \(\hat x\)

property y¶: Lagrange multipliers \(y\)

property Σ¶: Penalty factor \(\Sigma\)

property γ¶: Step size \(\gamma\)

property ε¶: Tolerance reached \(\varepsilon_k\)

property τ¶: Line search parameter \(\tau\)

property φγ¶: Forward-backward envelope \(\varphi_\gamma(x)\)

property ψ¶: Objective value \(\psi(x)\)

property ψ_hat¶

class alpaqa._alpaqa.PANOCSolver¶

C++ documentation: pa::PANOCSolver

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.PANOCSolver) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], lbfgs_direction: alpaqa._alpaqa.LBFGSDirection) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], lbfgs_params: Union[alpaqa._alpaqa.LBFGSParams, dict]) -> None
__init__(self: alpaqa._alpaqa.PANOCSolver, panoc_params: Union[alpaqa._alpaqa.PANOCParams, dict], direction: alpaqa._alpaqa.PANOCDirection) -> None

set_progress_callback(self: alpaqa._alpaqa.PANOCSolver, callback: Callable[[alpaqa._alpaqa.PANOCProgressInfo], None]) → None¶: Attach a callback that is called on each iteration of the solver.

property direction¶

property params¶

class alpaqa._alpaqa.PANOCStopCrit¶

C++ documentation: pa::PANOCStopCrit

Members:

ApproxKKT

ApproxKKT2

ProjGradNorm

ProjGradNorm2

ProjGradUnitNorm

ProjGradUnitNorm2

FPRNorm

FPRNorm2

Ipopt

__init__(self: alpaqa._alpaqa.PANOCStopCrit, value: int) → None¶

ApproxKKT = <PANOCStopCrit.ApproxKKT: 0>¶

ApproxKKT2 = <PANOCStopCrit.ApproxKKT2: 1>¶

FPRNorm = <PANOCStopCrit.FPRNorm: 6>¶

FPRNorm2 = <PANOCStopCrit.FPRNorm2: 7>¶

Ipopt = <PANOCStopCrit.Ipopt: 8>¶

ProjGradNorm = <PANOCStopCrit.ProjGradNorm: 2>¶

ProjGradNorm2 = <PANOCStopCrit.ProjGradNorm2: 3>¶

ProjGradUnitNorm = <PANOCStopCrit.ProjGradUnitNorm: 4>¶

ProjGradUnitNorm2 = <PANOCStopCrit.ProjGradUnitNorm2: 5>¶

property name¶

property value¶

class alpaqa._alpaqa.PGAParams¶

C++ documentation: pa::PGAParams

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.PGAParams) -> None
__init__(self: alpaqa._alpaqa.PGAParams, **kwargs) -> None

to_dict(self: alpaqa._alpaqa.PGAParams) → dict¶

property L_max¶

property L_min¶

property Lipschitz¶

property max_iter¶

property max_time¶

property print_interval¶

property quadratic_upperbound_tolerance_factor¶

property stop_crit¶

class alpaqa._alpaqa.PGAProgressInfo¶

C++ documentation: pa::PGAProgressInfo

__init__(*args, **kwargs)¶

property L¶

property fpr¶

property grad_ψ¶

property grad_ψ_hat¶

property k¶

property norm_sq_p¶

property p¶

property x¶

property x_hat¶

property y¶

property Σ¶

property γ¶

property ε¶

property ψ¶

property ψ_hat¶

class alpaqa._alpaqa.PGASolver¶

C++ documentation: pa::PGASolver

__call__(self: alpaqa._alpaqa.PGASolver, problem: alpaqa._alpaqa.Problem, Σ: numpy.ndarray[numpy.float64[m, 1]], ε: float, x: numpy.ndarray[numpy.float64[m, 1]], y: numpy.ndarray[numpy.float64[m, 1]]) → Tuple[numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], numpy.ndarray[numpy.float64[m, 1]], dict]¶

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(self: alpaqa._alpaqa.PGASolver, arg0: alpaqa._alpaqa.PGAParams) → None¶

set_progress_callback(self: alpaqa._alpaqa.PGASolver, callback: Callable[[alpaqa._alpaqa.PGAProgressInfo], None]) → None¶: Attach a callback that is called on each iteration of the solver.

property params¶

class alpaqa._alpaqa.Problem¶

C++ documentation: pa::Problem

__init__(self: alpaqa._alpaqa.Problem, n: int, m: int) → None¶

Parameters

n – Number of unknowns
m – Number of constraints

property C¶: Box constraints on \(x\)

property D¶: Box constraints on \(g(x)\)

property f¶: Objective funcion, \(f(x)\)

property g¶: Constraint function, \(g(x)\)

property grad_f¶: Gradient of the objective function, \(\nabla f(x)\)

property grad_g_prod¶: Gradient of constraint function times vector, \(\nabla g(x)\, v\)

property grad_gi¶: Gradient vector of the \(i\)-th component of the constriant function, \(\nabla g_i(x)\)

property hess_L¶: Hessian of the Lagrangian function, \(\nabla^2_{xx} L(x,y)\)

property hess_L_prod¶: Hessian of the Lagrangian function times vector, \(\nabla^2_{xx} L(x,y)\, v\)

property m¶: Number of general constraints, dimension of \(g(x)\)

property n¶: Number of unknowns, dimension of \(x\)

class alpaqa._alpaqa.ProblemWithCounters¶

C++ documentation: pa::ProblemWithCounters

See alpaqa._alpaqa.Problem for the full documentation.

__init__(self: alpaqa._alpaqa.ProblemWithCounters, problem: alpaqa._alpaqa.Problem) → None¶

property C¶

property D¶

property evaluations¶

property f¶

property g¶

property grad_f¶

property grad_g_prod¶

property grad_gi¶

property hess_L¶

property hess_L_prod¶

property m¶

property n¶

class alpaqa._alpaqa.ProblemWithParam¶

C++ documentation: pa::ProblemWithParam

See alpaqa._alpaqa.Problem for the full documentation.

__init__(*args, **kwargs)¶

property C¶

property D¶

property f¶

property g¶

property grad_f¶

property grad_g_prod¶

property grad_gi¶

property hess_L¶

property hess_L_prod¶

property m¶

property n¶

property param¶: Parameter vector \(p\) of the problem

class alpaqa._alpaqa.ProblemWithParamWithCounters¶

C++ documentation: pa::ProblemWithCounters

See alpaqa._alpaqa.Problem for the full documentation.

__init__(self: alpaqa._alpaqa.ProblemWithParamWithCounters, problem: alpaqa._alpaqa.ProblemWithParam) → None¶

property C¶

property D¶

property evaluations¶

property f¶

property g¶

property grad_f¶

property grad_g_prod¶

property grad_gi¶

property hess_L¶

property hess_L_prod¶

property m¶

property n¶

property param¶: Parameter vector \(p\) of the problem

class alpaqa._alpaqa.SolverStatus¶

C++ documentation: pa::SolverStatus

Members:

Unknown : Initial value

Converged : Converged and reached given tolerance

MaxTime : Maximum allowed execution time exceeded

MaxIter : Maximum number of iterations exceeded

NotFinite : Intermediate results were infinite or not-a-number

NoProgress : No progress was made in the last iteration

Interrupted : Solver was interrupted by the user

__init__(self: alpaqa._alpaqa.SolverStatus, value: int) → None¶

Converged = <SolverStatus.Converged: 1>¶

Interrupted = <SolverStatus.Interrupted: 6>¶

MaxIter = <SolverStatus.MaxIter: 3>¶

MaxTime = <SolverStatus.MaxTime: 2>¶

NoProgress = <SolverStatus.NoProgress: 5>¶

NotFinite = <SolverStatus.NotFinite: 4>¶

Unknown = <SolverStatus.Unknown: 0>¶

property name¶

property value¶

class alpaqa._alpaqa.StructuredPANOCLBFGSParams¶

C++ documentation: pa::StructuredPANOCLBFGSParams

__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSParams, **kwargs) → None¶

to_dict(self: alpaqa._alpaqa.StructuredPANOCLBFGSParams) → dict¶

property L_max¶

property L_min¶

property Lipschitz¶

property alternative_linesearch_cond¶

property full_augmented_hessian¶

property hessian_step_size_heuristic¶

property hessian_vec¶

property hessian_vec_finite_differences¶

property lbfgs_stepsize¶

property max_iter¶

property max_no_progress¶

property max_time¶

property nonmonotone_linesearch¶

property print_interval¶

property quadratic_upperbound_tolerance_factor¶

property stop_crit¶

property update_lipschitz_in_linesearch¶

property τ_min¶

class alpaqa._alpaqa.StructuredPANOCLBFGSProgressInfo¶

Data passed to the structured PANOC progress callback.

C++ documentation: pa::StructuredPANOCLBFGSProgressInfo

__init__(*args, **kwargs)¶

property L¶

property fpr¶

property grad_ψ¶

property grad_ψ_hat¶

property k¶

property norm_sq_p¶

property p¶

property x¶

property x_hat¶

property y¶

property Σ¶

property γ¶

property ε¶

property τ¶

property φγ¶

property ψ¶

property ψ_hat¶

class alpaqa._alpaqa.StructuredPANOCLBFGSSolver¶

C++ documentation: pa::StructuredPANOCLBFGSSolver

Solve.

Parameters

problem – Problem to solve
Σ – Penalty factor
ε – Desired tolerance
x – Initial guess
y – Initial Lagrange multipliers

Returns

Solution \(x\)
Updated Lagrange multipliers \(y\)
Slack variable error \(g(x) - z\)
Statistics

__init__(*args, **kwargs)¶

Overloaded function.

__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver) -> None
__init__(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver, panoc_params: Union[alpaqa._alpaqa.StructuredPANOCLBFGSParams, dict], lbfgs_params: Union[alpaqa._alpaqa.LBFGSParams, dict]) -> None

set_progress_callback(self: alpaqa._alpaqa.StructuredPANOCLBFGSSolver, callback: Callable[[alpaqa._alpaqa.StructuredPANOCLBFGSProgressInfo], None]) → None¶: Attach a callback that is called on each iteration of the solver.

property params¶

alpaqa._alpaqa.load_casadi_problem(so_name: str, n: int = 0, m: int = 0, second_order: bool = False) → alpaqa._alpaqa.Problem¶

Load a compiled CasADi problem without parameters.

C++ documentation: pa::load_CasADi_problem()

alpaqa._alpaqa.load_casadi_problem_with_param(so_name: str, n: int = 0, m: int = 0, p: int = 0, second_order: bool = False) → alpaqa._alpaqa.ProblemWithParam¶

Load a compiled CasADi problem with parameters.

C++ documentation: pa::load_CasADi_problem_with_param()

alpaqa._alpaqa.panoc(ψ: Callable[[numpy.ndarray[numpy.float64[m, 1]]], float], grad_ψ: Callable[[numpy.ndarray[numpy.float64[m, 1]]], numpy.ndarray[numpy.float64[m, 1]]], C: alpaqa._alpaqa.Box, x0: Optional[numpy.ndarray[numpy.float64[m, 1]]] = None, ε: float = 1e-08, params: alpaqa._alpaqa.PANOCParams = <alpaqa._alpaqa.PANOCParams object at 0x7f2437ac31f0>, lbfgs_params: alpaqa._alpaqa.LBFGSParams = <alpaqa._alpaqa.LBFGSParams object at 0x7f243cacc8f0>) → Tuple[numpy.ndarray[numpy.float64[m, 1]], dict]¶

Compile the objective and constraint functions into a alpaqa Problem.

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).

Returns

Problem specification that can be passed to the solvers.

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).

Returns

Code generator that generates the functions and derivatives used by the solvers.
Dimensions of the decision variables (primal dimension).
Number of nonlinear constraints (dual dimension).
Number of parameters.