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What (who) is integer optimization - definition
![[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name="MathWorld"/>](https://commons.wikimedia.org/wiki/Special:FilePath/Almost integer in triangle.svg?width=200 "[[Ed Pegg Jr.]] noted that the length ''d'' equals <math>\frac{1}{2}\sqrt{\frac{1}{30}(61421-23\sqrt{5831385})} </math> that is very close to 7 (7.0000000857 ca.)<ref name=\"MathWorld\"/>")
![negative]] integers are shown in blue and negative integers in red.](https://commons.wikimedia.org/wiki/Special:FilePath/Number-line.svg?width=200 "negative]] integers are shown in blue and negative integers in red.")
Wikipedia
An integer programming problem is a mathematical optimization or feasibility program in which some or all of the variables are restricted to be integers. In many settings the term refers to integer linear programming (ILP), in which the objective function and the constraints (other than the integer constraints) are linear.
Integer programming is NP-complete. In particular, the special case of 0-1 integer linear programming, in which unknowns are binary, and only the restrictions must be satisfied, is one of Karp's 21 NP-complete problems.
If some decision variables are not discrete, the problem is known as a mixed-integer programming problem.
