| 单词 | Mixed integer linear programming |
| 释义 |
Mixed integer linear programming
中文百科
线性规划 Linear programming（重定向自Mixed integer linear programming）
![线性规划](/Images/godic/202501/27/Linear_programming_polytope1528.png") 1529.png") ![](/Images/godic/202501/27/Progr_Lineal1529.PNG") ![A pictorial representation of a simple linear program with two variables and six inequalities. The set of feasible solutions is depicted in yellow and forms a polygon, a 2-dimensional polytope. The linear cost function is represented by the red line and the arrow: The red line is a level set of the cost function, and the arrow indicates the direction in which we are optimizing.](/Images/godic/202501/27/Linear_optimization_in_a_2-dimensional_polytope.svg1529.png") 在数学中，线性规划（Linear Programming，简称LP）特指目标函数和约束条件皆为线性的最优化问题。 线性规划是最优化问题中的一个重要领域。在作业研究中所面临的许多实际问题都可以用线性规划来处理，特别是某些特殊情况，例如：网络流、多商品流量等问题，都被认为非常重要。目前已有大量针对线性规划算法的研究。很多最优化问题算法都可以分解为线性规划子问题，然后逐一求解。在线性规划的历史发展过程中所衍伸出的诸多概念，创建了最优化理论的核心思维，例如「对偶」、「分解」、「凸集」的重要性及其一般化等。在微观经济学和商业管理领域中，线性规划亦被大量应用于例如降低生产过程的成本等手段，最终提升产值与营收。乔治·丹齐格被认为是线性规划之父。
英语百科
Linear programming 线性规划（重定向自Mixed integer linear programming）
![A closed feasible region of a problem with three variables is a convex polyhedron. The surfaces giving a fixed value of the objective function are planes (not shown). The linear programming problem is to find a point on the polyhedron that is on the plane with the highest possible value.](/Images/godic/202501/27/3dpoly.svg1529.png") ![Leonid Kantorovich](/Images/godic/202501/27/Leonid_Kantorovich_19751529.jpg") ![](/Images/godic/202501/27/Linear_Programming_Feasible_Region.svg1529.png") Linear programming (LP; also called linear optimization) is a method to achieve the best outcome (such as maximum profit or lowest cost) in a mathematical model whose requirements are represented by linear relationships. Linear programming is a special case of mathematical programming (mathematical optimization). |
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