Web Definition: Linear Programming
In mathematics, linear programming problems are optimization problems in which the objective function & the constraints are all linear. Linear programming is an important field of optimization for several reasons. Many practical problems in operations research can be expressed as linear programming problems. Certain special cases of linear programming, such as network flow problems & multicommodity flow problems are considered important enough to have generated much research on specialized algorithms for their solution. A number of algorithms for other types of optimization problems work by solving LP problems as sub-problems. Historically, ideas from linear programming have inspired many of the central concepts of optimization theory, such as duality, decomposition & the importance of convexity & its generalizations. Here is an example of a linear programming problem. Suppose that a farmer has a piece of farm land, say A square kilometres large, to be planted with either wheat or barley or some combination of the two.
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