contraints

Constraints are conditions that limit the possible values or actions within a system. They arise from physical laws, logical rules, resource limits, or policy requirements and are used to model what is feasible or acceptable. Understanding constraints helps in analysis, design, and decision making.

In mathematics and computer science, a constraint is a condition that a variable assignment must satisfy. Constraint satisfaction problems seek any assignment that meets all constraints. Common types include equality constraints (x = y), inequality constraints (x ≤ y), and bound constraints (a ≤ x ≤ b). In optimization, constraints restrict the domain of the objective function and can be equalities, inequalities, or integrality constraints.

In practical domains, constraints appear in scheduling, logistics, engineering, and data management. For example, in databases, constraints enforce data integrity through primary keys, foreign keys, unique, not null, and check constraints. In project management, the triple constraint (scope, time, cost) governs feasibility; adjusting one affects the others. In manufacturing, resource constraints limit production capacity.

Constraint handling includes methods such as constraint programming, relaxation, and approximation. Understanding and managing constraints is essential to ensure solutions are feasible, compliant, and efficient.