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Integer programming regards optimization problems, where one seeks to find integer values for a set of unknowns, that optimizes the objective function. A common subset of this type of problems are integer linear programming problems, where all inequalities, equalities and the objective function are linear in the unknowns.
2
votes
Some weird "system" of inequalities in nonnegative integers.
I see this as more of a set selection problem or a combinatorial design problem than a number theory problem, unless there is something else about the $a_{ijkl}$ that is not being mentioned.
By setti …
1
vote
Representing integer points inside a polytope using a unit hypercube
If a,b, and c are linearly independent over the rationals, then you can translate this problem by replacing the term involving f by a 3-tuple of integers and ask if you can find a basis "inside" D tha …