Feasible set

In mathematical optimization, a feasible region, feasible set, search space, or solution space is the set of all possible points (sets of values of the choice variables) of an optimization problem that satisfy the problem's constraints, potentially including inequalities, equalities, and integer constraints. This is the initial set of candidate solutions to the problem, before the set of candidates has been narrowed down.

For example, consider the problem

with respect to the variables ${\displaystyle x}$ and ${\displaystyle y,}$

subject to

and

Here the feasible set is the set of pairs (x, y) in which the value of x is at least 1 and at most 10 and the value of y is at least 5 and at most 12. Note that the feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is ${\displaystyle x^{2}+y^{4}.}$

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