Triangle inequality

Vector Calculus

Published in Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene, Modern Engineering Mathematics, 2017

Abul Hasan Siddiqi, Mohamed Al-Lawati, Messaoud Boulbrachene

The ‖ x + y ‖ ≤‖ x ‖ + ‖ y ‖ is called the triangle inequality. Consider the triangle formed by the points A = 0, B = x and C = x + y. The triangle inequality states that the length of the side connecting A and C cannot be larger than the sum of the length of the other two sides.

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Published in John D. Ross, Kendall C. Richards, Introductory Analysis, 2020

John D. Ross, Kendall C. Richards

The name “triangle inequality” comes from the notion that no side length of a triangle is larger than the sum of the lengths of its other two sides. The triangle inequality’s power comes from the fact that it can estimate the size of two quantities added together (|a + b|) by estimating the size of each quantity separately.

An efficient exact approach for the constrained shortest path tour problem

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Published in Optimization Methods and Software, 2020

Daniele Ferone, Paola Festa, Francesca Guerriero

Let be a weighted directed graph, where is a set of n nodes; is a set of m arcs; is a function that assigns a non-negative length or cost to each arc . The lengths do not necessarily satisfy the triangle inequality. Moreover, let denote N disjoint node subsets, that is , , .

Triangle inequality

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Vector Calculus

Preliminary Content

An efficient exact approach for the constrained shortest path tour problem