This note addresses computational difficulty of the Gromov-Wasserstein distance frequently mentioned in the literature. We provide details on the structure of the Gromov-Wasserstein distance optimization problem that show its non-convex quadratic nature for any instance of an input data. We further illustrate the non-convexity of the problem with several explicit examples.

翻译：本文针对文献中频繁提及的Gromov-Wasserstein距离计算困难问题进行探讨。我们详细分析了Gromov-Wasserstein距离优化问题的结构，证明对于任意输入数据实例，该问题均呈现非凸二次特性。通过多个具体示例，我们进一步阐明了该问题的非凸性质。