Feasible region

A feasible region is the set of points or values satisfying every constraint in an optimization problem. Its shape and boundaries depend on the constraints.

Decision variable: A variable whose value is chosen to solve an optimization problem. Decision variables specify the coordinates or values tested against the constraints.
Half-space (geometry): One of the two regions into which a plane divides space, including the plane itself when closed. A linear inequality selects one half-space of possible solutions.
Diet problem: A linear optimization problem that chooses foods to meet nutritional requirements at minimum cost. Nutrient requirements and food limits carve out the allowable combinations of foods.
Infeasible problem: An optimization problem with no point satisfying all its constraints. It has an empty feasible region, so no admissible solution exists.
Constraint (mathematics): A condition that restricts the allowed values of variables in a mathematical problem. Each constraint removes points that violate a required condition.
Intersection (set theory): The set of elements that belong to every one of a collection of sets. The feasible region is the intersection of the sets allowed by individual constraints.
Transportation problem: An optimization problem that allocates shipments from sources to destinations at minimum cost. Supply, demand, and nonnegativity constraints define feasible shipment plans.
Unbounded problem: An optimization problem whose objective can improve without limit over its feasible solutions. A nonempty feasible region can still lack a finite optimum if it extends in an improving direction.
Inequality: A mathematical statement comparing quantities with symbols such as <, ≤, >, or ≥. Inequalities commonly define the half-spaces whose intersection forms a feasible region.
Convex set: A set containing the entire line segment between any two of its points. Feasible regions defined by convex constraints are themselves convex.

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