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[[Category:Chart, diagram and graph templates]] to the <includeonly> section at the bottom of that page. Otherwise, add <noinclude>[[Category:Chart, diagram and graph templates]]</noinclude> to the end of the template code, making sure it starts on the same line as the code's last character.
Two-dimensional linear inequalities are expressions in two variables of the form: + < +, where the inequalities may either be strict or not. The solution set of such an inequality can be graphically represented by a half-plane (all the points on one "side" of a fixed line) in the Euclidean plane. [2]
Jensen's inequality generalizes the statement that a secant line of a convex function lies above its graph. Visualizing convexity and Jensen's inequality. In mathematics, Jensen's inequality, named after the Danish mathematician Johan Jensen, relates the value of a convex function of an integral to the integral of the convex function.
If a connected graph is a Cartesian product, it can be factorized uniquely as a product of prime factors, graphs that cannot themselves be decomposed as products of graphs. [2] However, Imrich & Klavžar (2000) describe a disconnected graph that can be expressed in two different ways as a Cartesian product of prime graphs:
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 optimum of the linear cost function is where the red line intersects the polygon.
An acyclic graph is a forest, but connectedness is usually assumed; as a result, the condition that is usually considered is that primal graphs are trees. This property of tree-like constraint satisfaction problems is exploited by decomposition methods , which convert problems into equivalent ones that only contain binary constraints arranged ...