We implement an Augmented Lagrangian method to minimize a constrained least-squares cost function designed to find polyadic decompositions of the matrix multiplication tensor. We use this method to obtain new discrete decompositions and parameter families of decompositions. Using these parametrizations, faster and more stable matrix multiplication algorithms can be discovered.

翻译：我们实现了一种增广拉格朗日方法，用于最小化一个旨在寻找矩阵乘法张量多adic分解的约束最小二乘代价函数。利用该方法，我们获得了新的离散分解及参数化分解族。通过这些参数化表示，可以发现更快且更稳定的矩阵乘法算法。