awesome-inequality

A curated list of inequalities in our life

Book

The Cauchy-Schwarz Master Class: An Introduction to the Art of Mathematical Inequalities

https://www.maa.org/press/maa-reviews/the-cauchy-schwarz-master-class-an-introduction-to-the-art-of-mathematical-inequalities

Use cases

Hoeffding's inequality

Used to derive confidence interval in approximate query processing.

Jensen's inequality

Used to derive tractable lower bound of model evidence in variational Bayesian inference (variational auto encoders also).

Triangle inequality

Basis of spatial indexing methods. Can reduce the number of candidates in similarity search.

Cauchy–Schwarz inequality

Can be used to approximate dot product and prune candidates in similarity search.

Holder's_inequality

Generalization of Cauchy–Schwarz inequality.