boundlab.gradlin

Batched trapezoid linearization for unary functions.

gradlin() estimates (lam_x, lam_y) and bounds L, U for

f(x) - f(y) - lam_x * x - lam_y * y

over the batched trapezoid

lx <= x <= ux, ly <= y <= uy, ld <= x - y <= ud.

The solver first samples points to fit the slopes and then uses Adam to search for extremal residuals.

Example

>>> import torch
>>> from boundlab.gradlin import gradlin, trapezoid_region
>>> lx = torch.tensor([-1.0]); ux = torch.tensor([1.0])
>>> ly = torch.tensor([-1.0]); uy = torch.tensor([1.0])
>>> ld = torch.tensor([-2.0]); ud = torch.tensor([2.0])
>>> f = lambda x: torch.exp(x)
>>> lam, L, U = gradlin(f, lx, ux, ly, uy, ld, ud, num_samples=128, iters=10)

Functions

gradlin	Estimate lam_x, lam_y, L, U for a batched trapezoid.
trapezoid_region	Build box bounds + diff-constraint rows for the 2D trapezoid.