MinMapComplementarity#

Source: models/common/MinMapComplementarity.py

KKT complementarity condition enforced with the minimum map.

The complementarity conditions $a \ge 0, b \ge 0, ab = 0$ are equivalent to the single scalar equation $$r = \min(a, b) = 0.$$ The residual is piecewise-linear: it equals whichever of the two arguments is currently smaller, a hard switch that gives semismooth-Newton / active-set behavior and converges robustly in return mapping. The switch is selected per batch entry with ``where`` (no Python branching), so the model lowers through AOTI and runs on GPU; the trade-off is a piecewise-constant Jacobian that is non-smooth at the switch $a = b$.

The sign of each argument follows its declared inequality: LE enforces $\le 0$ (coefficient $-1$) and GE enforces $\ge 0$ (coefficient $+1$), so the enforced residual is $r = \min(s_a\, a,\; s_b\, b)$.

Inputs#

a — input · Scalar · required: First condition
b — input · Scalar · required: Second condition

Outputs#

complementarity — output · Scalar · required: The minimum-map complementarity condition

Other options#

a_inequality — str · default LE: Type of the inequality for the first variable a.
b_inequality — str · default GE: Type of inequality for the second variable b.