constraint

A constraint is a limitation or restriction that defines what is permissible or possible within a system, problem, or process. Constraints influence decisions, outcomes, and the allocation of resources. They may be external, such as physical laws or policy requirements, or internal, such as design goals or performance targets.

In mathematics and optimization, constraints are conditions specified on variables that define a feasible set. They can be equalities or inequalities. A problem is solved by finding a value that satisfies all constraints; optimization seeks the best value within the feasible region, often using methods like Lagrange multipliers or linear programming.

In computer science and information systems, constraint programming solves problems by declaring constraints and using a solver to search for assignments that satisfy them. In databases and data management, constraints enforce data integrity, including domain constraints, primary keys, foreign keys, and check constraints that enforce rules on column values.

In engineering and design, constraints reflect limits on resources, timing, safety, and compatibility with existing systems. Design processes often involve trade-offs among conflicting constraints, balancing performance, cost, and feasibility.

Constraint handling and solving strategies include relaxation (loosening constraints), constraint propagation, decomposition, and approximation. In some contexts, constraints are treated as objectives to be minimized or achieved within acceptable margins, as in robust optimization. Examples of constraints include resource limits, budgets, time frames, and capacity restrictions.