Optimization Methods#

Overview#

Non-Negative Least Squares#

Pseudo Projected Gradient Descent#

Projected Graident Descent#

Like Pseudo-PGD, but performs orthogonal projection onto unit simplex

Automatic Gradient Descent#

Parameters#

Numpy backend#

Non-Negative Least Squares (nnls):

Parameter	Type	Default	Description
`max_iter_optimizer`	int	100	The maximum number of iterations in the nnls optimization, passed to `scipy.optimize.nnls`
`const`	float	100.0	The penalization constant to add in the nnls optimization to enforce convex optimization.

(Pseudo) Projected Gradient Descent (pgd and pseudo_pgd):

Parameter	Type	Default	Description
`max_iter_optimizer`	int	10	The maximum number of iterations for optimizing the learning rate.
`beta`	float	0.5	The decay factor for the learning rate.
`step_size`	float	1.0	The initial learning rate at the beginning of optimization, corresponding to the objective function $\frac{1}{2} \left\lVert X - A B X \right \rVert^2$

JAX backend#

Automatic Gradient Descent (autogd):

Parameter	Type	Description
`optimizer`	str or optax.GradientTransformation	The optimization method to use. See the available optimizers.
`optimizer_kwargs`	dict	The arguments to pass to initialize the optimization method.

Torch backend#

Automatic Gradient Descent (autogd)

Parameter	Type	Description
`optimizer`	str or torch.optim.Optimizer	The optimization method to use. See the available optimizers.
`optimizer_kwargs`	dict	The arguments to pass to initialize the optimization method.