inequalitythat

Inequalitythat is a coined term used to describe a class of inequality constraints that are activated only under specific conditions or contexts. It is not a standard mathematical designation, but it appears in discussions of conditional or regime-dependent modeling to illustrate how inequalities can govern behavior in particular scenarios.

Formally, an inequalitythat can be described as a conditional constraint of the form C(x) implies f(x) ≤ 0, where C(x) is a condition depending on the decision variables or parameters. When the condition C(x) is true, the inequality f(x) ≤ 0 must hold; when C(x) is false, the constraint is effectively inactive. In optimization practice, such conditional constraints are often implemented with indicator variables, disjunctive programming, or big-M formulations to enforce the inequality only in the active regime.

Typical characteristics include: conditional applicability, a piecewise or regime-based structure, and relevance to models that reflect policy triggers, safety limits, or resource thresholds. They are commonly used in operations research, economics, energy systems, and engineering to model rules that apply only under certain states of the system.

Examples include: if inventory s ≥ S, then production p ≤ P; or if demand d exceeds threshold T, then price q must satisfy q ≥ Q to ensure supply adequacy. In both cases the inequality binds only when the predefined condition holds.

Related concepts include conditional constraints, indicator constraints, and disjunctive programming. See also optimization under uncertainty and piecewise linear models.