Quadratic Positive Part

QuadraticPositivePartFunction gives both implementations the same unambiguous operation:

$$y=max\{p(x),0\}.$$

This is a positive-part function, not a semi-continuous variable. The old Rust name QuadraticSemiFunction has been removed. Semi-continuous domains remain the responsibility of the separate linear SemiFunction API.

Solver mathematical model

Kotlin

Kotlin uses the identity $y=-min\{-p(x),0\}$. Let $t=min\{-p(x),0\}$ and $u_0,u_1\in \{0,1\}$. Its exact selector model is:

$$\begin{array}{rl}t& \le -p(x),\\ t& \le 0,\\ t& \ge -p(x)-M(1-u_0),\\ t& \ge -M(1-u_1),\\ u_0+u_1& =1,\\ y& =-t.\end{array}$$

The public quadratic result expression is -resultVar; resultVar itself is the internal minimum $t$.

Rust

Rust first bridges the quadratic input as $b=p(x)$ and then applies an exact two-candidate maximum:

$$\begin{array}{rl}b& =p(x),\\ y& \ge b,\\ y& \ge 0,\\ y& \le b+M(1-u_0),\\ y& \le M(1-u_1),\\ u_0+u_1& =1.\end{array}$$

The formulations differ internally but define the same result and direct-evaluation contract.

API and examples

Kotlin

val p = QuadraticPolynomial(
    monomials = listOf(QuadraticMonomial.quadratic(Flt64.one, x, x)),
    constant = -Flt64(4.0)
)
val positivePart = QuadraticPositivePartFunction(
    input = p,
    bigM = Flt64(100.0),
    converter = IntoValue.Identity,
    name = "positive_part"
)
// x = 1: max(1^2 - 4, 0) = 0

Rust

let p = Quadratic::new(
    vec![QuadraticMonomial::new_quadratic(1.0, x_index, x_index)],
    -4.0,
);
let positive_part = QuadraticPositivePartFunction::new(
    17,
    "positive_part",
    p,
);
// x = 1: max(1^2 - 4, 0) = 0

Kotlin accepts an optional explicit bigM; otherwise it derives candidate-specific values from finite polynomial bounds. Rust derives the selector Big-M from registered token bounds when possible and otherwise uses its configured fallback.

Evaluation and boundaries

Direct evaluation returns zero for a negative input, the input for a positive value, and zero at the origin. Missing input values return null/None. This arithmetic function has no tolerance-based Undefined region.

Tests and source

• Kotlin source: QuadraticPositivePart.kt
• Kotlin independent test: QuadraticPositivePartFunctionTest.kt
• Rust source: quadratic_function.rs
• Rust independent test: function_symbol_quadratic_positive_part.rs

Related pages

• Linear semi-continuous marker
• Quadratic minimum