Here we present a center-cut algorithm for convex mixed-integer nonlinear programming (MINLP) that can either be used as a primal heuristic or as a deterministic solution technique. Like several other algorithms for convex MINLP, the center-cut algorithm constructs a linear approximation of the original problem. The main idea of the algorithm is to use the linear approximation differently in order to find feasible solutions within only a few iterations. The algorithm chooses trial solutions as the center of the current linear outer approximation of the nonlinear constraints, making the trial solutions more likely to satisfy the constraints. The ability to find feasible solutions within only a few iterations makes the algorithm well suited as a primal heuristic, and we prove that the algorithm finds the optimal solution within a finite number of iterations. Numerical results show that the algorithm obtains feasible solutions quickly and is able to obtain good solutions.

在这里，我们提出了凸混合整数非线性规划（MINLP）的中心切割算法，该算法既可以用作原始启发式算法，也可以用作确定性求解技术。与凸MINLP的其他几种算法一样，中心切割算法可构造原始问题的线性近似。该算法的主要思想是不同地使用线性逼近，以便仅在几次迭代中找到可行的解。该算法选择试验解作为非线性约束的当前线性外部近似的中心，从而使试验解更有可能满足约束。只需几次迭代即可找到可行解决方案的能力使该算法非常适合作为原始启发式算法，并且我们证明了该算法在有限数量的迭代中找到了最优解。数值结果表明，该算法能够快速获得可行解，并且能够获得良好的解。