Semi-Continuous Variable

SemiFunction<V> models a variable that is either zero or lies in the active interval [lb, ub].

Solver mathematical model

The symbol creates a continuous result $y$ and a binary activation variable $b$. The rows sent to the solver are

$$y-ubb\le 0,y-lbb\ge 0.$$

When $b=0$, these rows force $y=0$; when $b=1$, they enforce $lb\le y\le ub$. The constructor validates lb <= ub and the result and indicator are registered as auxiliary variables.

Kotlin API

val semi = SemiFunction(
    lb = Flt64(2.0),
    ub = Flt64(5.0),
    converter = IntoValue.Identity,
    name = "semi"
)

SemiFunction.from(variable, ...) infers missing finite bounds from a continuous variable. resultVar, indicatorVar, and resultPolynomial expose the model representation.

Rust API

let semi = SemiFunction::new(1, "semi", 2.0_f64, 5.0_f64);
assert!(semi.result_variable().name().contains("semi"));

Rust also provides try_from_variable/from_variable for finite-bound inference. Both implementations register the same two domain rows.

Kotlin/Rust example

Kotlin

val semi = SemiFunction(
    lb = Flt64(2.0),
    ub = Flt64(5.0),
    converter = IntoValue.Identity,
    name = "semi"
)
check(semi.helperVariables.size == 2)

Rust

let semi = SemiFunction::new(1, "semi", 2.0_f64, 5.0_f64);
assert_eq!(semi.lower_bound(), &2.0);
assert_eq!(semi.upper_bound(), &5.0);

Tests and references

• Kotlin focused test: SemiFunctionDedicatedTest.kt
• Kotlin regression test: SemiFunctionTest.kt
• Kotlin implementation: Semi.kt
• Rust implementation: semi.rs
• Rust focused test: function_symbol_semi.rs

The focused tests assert both helper tokens and both registered domain rows, plus the shared default interval and eager reversed/non-finite bound validation.

Bounds are validated eagerly and must be finite with lower no greater than upper. Omitting Kotlin bounds uses the shared interval [0, 1e6]; Rust exposes SemiFunction::with_default_bounds for the same interval. Missing token values remain explicit: Kotlin returns null, while Rust follows zero_if_none.