Euclidean distance matrices have lately received increasing attention in applications such as multidimensional scaling and molecular conformation from nuclear magnetic resonance data in computational chemistry. In this paper, we focus on the perturbation analysis of the Euclidean distance matrix optimization problem (EDMOP). Under Robinson’s constraint qualification, we establish a number of equivalent characterizations of strong regularity and strong stability at a locally optimal solution of EDMOP. Those results extend the corresponding characterizations in Semidefinite Programming and are tailored to the special structure in EDMOP. As an application, we demonstrate a numerical implication of the established results on an alternating direction method of multipliers (ADMM) to a stress minimization problem, which is an important instance of EDMOP. The implication is that the ADMM method converges to a strongly stable solution under reasonable assumptions.

欧几里德距离矩阵最近在计算化学中的多维标度和核磁共振数据的分子构象等应用中受到越来越多的关注。在本文中，我们重点关注欧几里德距离矩阵优化问题（EDMOP）的扰动分析。在Robinson约束条件下，我们在EDMOP的局部最优解上建立了许多强规律性和强稳定性的等价表征。这些结果扩展了半定规划中的相应特征，并针对 EDMOP 中的特殊结构进行了定制。作为一个应用，我们展示了乘子交替方向法 (ADMM) 的既定结果对应力最小化问题的数值含义，这是 EDMOP 的一个重要实例。