# How literally is “optimization” or “optimization algorithm” used in CS?

I have been confronted with two meanings of the term "optimization" or "optimization algorithm":

1. to find the absolute maximum in a set $$X$$ according to some criterion $$f:X\to \mathbb R$$

2. to find a "relatively high" or "increasingly high" or "locally maximum" element in a set $$X$$ according to some criterion $$f:X\to \mathbb R$$

A friend of mine claimed that nr $$1$$. is the only "official" meaning of the term, and that only laymen or people who speak informally use the meaning of $$2$$. Is my friend correct?

• There’s no official dictionary of computer science. – Yuval Filmus Dec 29 '18 at 8:24
• Approximation algorithms are definitely part of optimization. – Yuval Filmus Dec 29 '18 at 8:25
• @YuvalFilmus, I put "official" between quotes for a reason. – user626625 Dec 29 '18 at 19:24
• Finding a local minimum or maximum definitely counts as optimization. For example, we use optimization algorithms to train neural networks, and these algorithms find local minimums, not global minimums. – littleO Dec 29 '18 at 23:17