Granularity for Mixed-Integer Polynomial Optimization Problems
针对混合整数规划中寻找可行点困难的问题，提出一种称为“粒度性”的充分条件，结合多项式优化的矩/平方和层级方法，通过求解连续多项式问题并取整得到可行点，数值实验验证了有效性。
Abstract Finding good feasible points is crucial in mixed-integer programming. For this purpose we combine a sufficient condition for consistency, called granularity, with the moment-/sum-of-squares-hierarchy from polynomial optimization. If the mixed-integer problem is granular, we obtain feasible points by solving continuous polynomial problems and rounding their optimal points. The moment-/sum-of-squares-hierarchy is hereby used to solve those continuous polynomial problems, which generalizes known methods from the literature. Numerical examples from the MINLPLib illustrate our approach.