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We consider the integer Chebyshev problem, that of minimizing the supremumnorm over polynomials with integer coefficients on the interval $[0,1]$. Weimplement algorithms from semi-infinite programming and a branch and boundalgorithm to improve on previous methods for finding integer Chebyshevpolynomials of degree $n$. Using our new method, we found 16 new integerChebyshev polynomials of degrees in the range 147 to 244.

Applications of Integer and Semi-Infinite Programming to the Integer Chebyshev Problem