In numerical optimization, what defines a feasible region?

The feasible region in numerical optimization is defined as the set of all points that satisfy the constraints of the problem. These constraints can be equalities or inequalities that outline the limits within which a solution can be found.

In practical terms, when you graph these constraints, the feasible region represents the area where all conditions imposed by the constraints are met. This region is crucial because any optimization algorithm seeks to find the optimal solution—such as maximizing or minimizing a particular objective function—within this bounded area.

Understanding the feasible region is essential because it directly influences the solution space of the optimization problem. If a point lies within this region, it is a candidate for being an optimal solution, whereas points outside this region are not viable options since they do not adhere to the defined constraints.