A real-valued function defined on an interval with the property that its epigraph—the collection of points on or above the function's graph—is a convex set—is said to be convex. The challenge of minimizing convex functions over convex sets is the subject of the optimization discipline known as convex minimization.
A mathematical model whose needs are expressed by linear connections can be optimized using a technique known as linear programming. A particular type of mathematical programming is linear programming. When a linear function is subjected to various constraints, it is maximized or minimized using the mathematical modeling technique known as linear programming. In business planning, industrial engineering, and—to a lesser extent—the social and physical sciences, this method has proven helpful for directing quantitative decisions.
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