Constrained

Constrained is the past participle and adjective of constrain, meaning restricted, limited, or bound by rules or conditions. In general use, something is constrained when it must operate within predefined bounds or under specific requirements.

In mathematics and optimization, a constrained problem specifies variables that must satisfy certain conditions called constraints. These can be equalities or inequalities. The feasible set comprises all points that meet constraints. Solving involves finding extrema or feasible solutions within that set. Common techniques include Lagrange multipliers, penalty and barrier methods, and projection algorithms. Constrained dynamics study systems whose motion is limited by constraints, such as rigid bodies connected by joints, leading to holonomic or nonholonomic constraints.

In computer science, constraint programming models problems as variables with domains and a set of constraints; a solution assigns values to variables that satisfy all constraints. Constraint satisfaction problems are central in scheduling, resource allocation, and puzzle solving.

Linguistically and in social contexts, constraints describe rules that govern possible sentences or actions; for example, syntactic constraints limit acceptable word orders. The term conveys limits that reduce freedom of choice.

Etymology: constrained derives from constraint, which traces to the Latin constringere, meaning to bind together.