Expand description
Differentiable Linear Programming.
Solves the LP:
min c’x s.t. Ax = b (p equalities) Gx ≤ h (m inequalities)
and computes gradients of x* w.r.t. (c, A, b, G, h) via implicit differentiation through the KKT conditions at the active constraints.
At an LP optimum, the active inequality constraints define a polyhedron face. We differentiate as if solving the equality-constrained system formed by the active set, which is a degenerate QP with Q = 0 (plus regularization for numerical stability).
Structs§
- DifferentiableLP
- A differentiable LP layer.