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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 :Minimize with respect to the variables and 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 In many problems, the feasible set reflects a constraint that one or more variables must be non-negative. In pure integer programming problems, the feasible set is the set of integers (or some subset thereof). In linear programming problems, the feasible set is a convex polytope: a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices. Constraint satisfaction is the process of finding a point in the feasible region. ==Convex feasible set== A convex feasible set is one in which a line segment connecting any two feasible points goes through only other feasible points, and not through any points outside the feasible set. Convex feasible sets arise in many types of problems, including linear programming problems, and they are of particular interest because, if the problem has a convex objective function that is to be maximized, it will generally be easier to solve in the presence of a convex feasible set and any local optimum will also be a global optimum. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Feasible region」の詳細全文を読む スポンサード リンク
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