We construct an algorithm for the accurate solution of mixed integer convex quadratic programming, which is the problem of minimizing a convex quadratic function over mixed integer points in a polyhedron. Our algorithm is fixed parameter tractable with parameter the number of integer variables. In particular, when the number of integer variables is fixed, the running time of our algorithm is bounded by a polynomial of the size of the problem. To design our algorithm, we prove a number of fundamental structural and algorithmic results for mixed integer linear and quadratic programming.

翻译：我们构建了一种精确求解混合整数凸二次规划的算法，该问题旨在多面体中的混合整数点上最小化凸二次函数。我们的算法是固定参数可解的，参数为整数变量的数量。特别地，当整数变量数量固定时，算法运行时间受问题规模的多项式界限约束。为设计该算法，我们证明了混合整数线性与二次规划的一系列基础性与算法性结构结果。