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Combinatorial optimization typically deals with optimizing over a finite set of objects that have some combinatorial structure (e.g. trees, matchings, matroids). Approximation algorithms, polyhedral methods, and integer programming are all on topic.

2 votes

Does general case of following function exist?

After a bit of playing around I found a solution for $3$ variables: $$f_3(x,y,z)=\frac{1}{6}\Bigl(2xyz + (xy+ xz -2yz) + (2x -y-z)-2\Bigr).$$ When you check the conditions you see that when summing up …
Adam Zsolt Wagner's user avatar