In this paper we show that simple projections can improve the algorithmic performance of cutting plane-based optimization methods. Projected cutting planes can, for example, be used as alternatives to standard cutting planes or supporting hyperplanes in the extended cutting plane (ECP) method. In the paper we analyse the properties of such an algorithm and prove that it will converge to a global optimum for smooth and nonsmooth convex mixed integer nonlinear programming problems. Additionally, we show that we are able to solve two old but very difficult facility layout problems (FLP), with previously unknown optimal solutions, to verified global optimum by using projected cutting planes in the algorithm. These solution results are also given in the paper.

在本文中，我们展示了简单的投影可以提高基于切割平面的优化方法的算法性能。例如，在扩展切割平面 (ECP) 方法中，投影切割平面可以用作标准切割平面或支持超平面的替代方案。在本文中，我们分析了这种算法的特性，并证明它会收敛到光滑和非光滑凸混合整数非线性规划问题的全局最优解。此外，我们表明我们能够解决两个古老但非常困难的设施布局问题 (FLP)，使用以前未知的最佳解决方案，通过在算法中使用投影切割平面来验证全局最优。论文中也给出了这些求解结果。