Newton
Newton(HP=NewtonParameters(), verbose=NewtonVerboseOptions(), **kwargs)
Bases: Logger
Newton's algorithm to find the minimum of a function knowing its gradient and hessian.
References
[1] https://won-j.github.io/M1399_000200-2021fall/lectures/22-newton/newton_constr.html
optimize(x_init)
Alias of the 'run' method.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
x_init
|
ndarray
|
initial values for the variables. |
required |
Returns:
| Name | Type | Description |
|---|---|---|
float |
float
|
final value of the energy |
register_constraints(A, l=None, u=None)
Adds linear constraints to the optimization problem :
min_X F(X) s.t. l <= AX <= u
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
cstMat
|
spmatrix
|
constraint matrix, either dense or sparse |
required |
cstL
|
ndarray
|
vector l. Defaults to None. |
required |
cstR
|
ndarray
|
vector u. Defaults to None. |
required |
register_function(fun, fun_noG=None)
Adds a function to minimize.
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
fun
|
python callable
|
A function taking a single argument X (np.array) returning a real value F, a gradient G and a hessian matrix H |
required |
fun_noG
|
python callable
|
The same function that avoids the computation of the gradient and the hessian for speed purposes. If not provided, will use the function provided above and ignore the other arguments. |
None
|
run(x_init)
Runs the optimizer
Parameters:
| Name | Type | Description | Default |
|---|---|---|---|
x_init
|
ndarray
|
initial values for the variables. |
required |
Returns:
| Name | Type | Description |
|---|---|---|
float |
final value of the energy |
NewtonParameters(N_ITER_MAX=1000, MIN_STEP_NORM=1e-06, MIN_DELTA_F=1e-08, MIN_GRAD_NORM=1e-08, alpha_init=1.0, c1=0.0001, rho=0.5)
dataclass
Hyper parameters for Newton's algorithm