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We construct an algorithm for the accurate solution of mixed integer convexquadratic programming, which is the problem of minimizing a convex quadraticfunction over mixed integer points in a polyhedron. Our algorithm is fixedparameter tractable with parameter the number of integer variables. Inparticular, when the number of integer variables is fixed, the running time ofour algorithm is bounded by a polynomial of the size of the problem. To designour algorithm, we prove a number of fundamental structural and algorithmicresults for mixed integer linear and quadratic programming.

Mixed Integer Convex Quadratic Programming is Fixed Parameter Tractable