What is the difference between optimal and optimum?


My question is exactly as the title says. Someone used "optimum" in an email to me and in my response I used "optimal," so I began wondering what the difference between them is.



Answer



I'd like to add the following lines as an addendum to other answers.


In some areas of mathematics, an optimal value is essentially a local optimum; i.e. it's an optimum value in its neighborhood. For example:


local optimum example


In parallel, the same applies to maximal and minimal values. In other words, a maximal value is essentially a local maximum; a minimal value is essentially a local minimum. For example:


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