“linear programming”的概念、定义、习题解题方法及翻译-数学辞典

单词

linear programming

释义

linear programming

The branch of mathematics concerned with maximizing or minimizing a linear function subject to a number of linear constraints. It has applications in economics, industry, and commerce, for example. In its simplest form, with two variables, the constraints determine a feasible region, which is the interior of a polygon in the plane. The objective function to be maximized or minimized attains its maximum or minimum value at a vertex of the feasible region. For example, consider the problem of maximizing 4x1−3x2 subject to

The feasible region is the interior of the polygon OABCD shown in the figure, and the objective function 4x1−3x2 attains its maximum value of 17 at the point B with coordinates (5, 1).

The feasible region

Often integer values are required, and in such cases the vertex is not always admissible and it will be necessary to test all points with integer values which lie close to the vertex. It is also possible that the objective function may be parallel to a constraining condition. In this case, all points on the boundary representing that constraint will be optimal.

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