ENH: LinearOperator for linprog arguments A_ub and A_eq

Is your feature request related to a problem? Please describe.

The estimation of linear quantile regression can be recast as a linear programming problem with equality matrix

n_samples = X.shape[0]
A_eq = np.concatenate(
                [X, -X, np.eye(n_samples), -np.eye(n_samples)], axis=1
            )

where X is the feature matrix (predict will give X @ coef), see https://github.com/scikit-learn/scikit-learn/blob/0d378913be6d7e485b792ea36e9268be31ed52d0/sklearn/linear_model/_quantile.py#L203-L217.

This could help to save computation time and memory.

Describe the solution you’d like.

I’d like be able to pass a scipy.sparse.linalg.LinearOperator to linprog as argument A_ub and A_eq.

Describe alternatives you’ve considered.

No response

Additional context (e.g. screenshots, GIFs)

No response

[jajhall]

Where would the documentation and examples be?

In the scipy docu of linprog. Something like: “There is no need to formulate a linear programming problem in terms of positive variables. The solvers accept general bounds for x and might even be more efficient this way.”

A further doc improvement could be to say, that highs as well as interior-point, in the end, work on csc matrices.

I see what you mean now. Thanks. Been a productive discussion for me, but I think it’s run its course. Cheers Julian

[jajhall]

No, HiGHS cannot handle anything other than an actual sparse matrix.

It’s conceivable that the simplex solver could be adapted to handle an abstracted linear operator as a means of obtaining columns of the implied constraint matrix, and performing matrix-vector products. However, a square submatrix of the constraint matrix would have to be formed periodically as an actual sparse matrix, so some overhead comparable to supplying the whole matrix in that form would be inevitable unless the whole matrix has overwhelmingly more columns than rows.

Although it’s an interesting challenge, incorporating it would be a lot of work, for which resources are currently unavailable. Thus, whoever wanted it would have to come up with a lot of cash!