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lp_gradient

scirs2_optimize::differentiable_optimization::lp_layer

Function lp_gradient 

Source 
pub fn lp_gradient(
    c: &[f64],
    a: &[Vec<f64>],
    b: &[f64],
    x_star: &[f64],
    dl_dx: &[f64],
    epsilon: f64,
) -> OptimizeResult<Vec<f64>>
Expand description

Compute the gradient dL/dc for the entropy-regularized LP.

For the perturbed LP, the Jacobian of x* w.r.t. c is:

dx*/dc = -(1/ε) diag(x*) (I - 1ᵀ x* / Σ x*)

(from the softmax Jacobian, where x* = softmax(-c/ε)/ Σ x*).

The gradient dL/dc_i = Σ_j (dx*/dc)_{ji} * dL/dx_j.

For the simple case without constraints: dx*/dc = -(1/ε)(diag(x*) - x* x*ᵀ).