Scaled

Scaled multiplies an entire penalty, including its existing strengths:

For $a > 0$, its exact proximal map is the inner penalty's map with step $sa$. For $a = 0$, it returns zero cost and the identity proximal map, while still validating the inner parameters and dimensions.

Constraint region

Top: L1::new(1.0). Bottom: Scaled::new(2.0, L1::new(1.0)). At budget one, doubling L1 halves each intercept of its diamond. A zero multiplier makes the entire plane feasible. See the plot conventions.

Use the wrapper

use shrinkage::{L1, Penalty, ProximalPenalty, Scaled};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let penalty = Scaled::new(2.0, L1::new(0.5));
    assert_eq!(penalty.value(&[2.0, -1.0])?, 3.0);
    let mut shrunk = [0.0; 2];
    penalty.prox(&[2.0, -1.0], 1.0, &mut shrunk)?;
    assert_eq!(shrunk, [1.0, 0.0]);
    Ok(())
}

The multiplier must be finite and nonnegative. Scaling a value-only term does not supply an exact proximal map. A scaled built-in proximal penalty supports proximal gradient, but the wrapper does not add coordinate, IRLS, or hybrid compatibility. Compose it inside AxisPenalty for matrix coefficients.

API: shrinkage::Scaled.