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All theories I know of in mathematics define at some point the object concerned (graph theory, information theory, ...). Except for one : mathematical programming.

There are in it definitions of linear programming, integer programming, quadratic programming... One could eventually define mathematical programming as the most general case, mixed integer non linear programming. However, I have not seen it ever done in any book. Is there a particular reason for this ? Or did I miss something ? Is it an undefined word we just use to save time ?

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    It refers to optimization. I suspect the term originated in operations research. – 2017-02-20
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    Well, the problem of mathematical programming is to maximize some objective function under some constraints. The term programming comes, I think, from military terminology; the original work on linear programming came from Dantzig work for Air force. – 2017-02-20
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    @copper.hat That we can be sure of, but it is used all the time in the field without being defined – 2017-02-20
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    I have never seen it explicitly defined. I think the term programming was used to mean arranging or scheduling (as in sequence of events in a factory, for example). – 2017-02-20
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    Well, isn't a "program" simply a function $f : A \to \mathbb{R}$, which can be maximized (minimized)? Or the answer is, a "mathematical program" isn't really a mathematical thing. – 2017-02-20
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    Mathematical programming is essentially optimization under constraints, isn't it ? – 2017-02-20

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