This paper presents a sparse optimization method for the simultaneous orthogonal tensor diagonalization. The model treats off-diagonal elements of tensors as entities requiring sparsity, guided by an ℓ1 norm regularizer to optimize the diagonalization process. A gradient-based alternating multi-block Jacobi-AMB algorithm is developed to address the optimization problem on the product of orthogonal groups. We establish the global convergence based on the Kurdyka-Łojasiewicz property. Numerical experiments demonstrate that the Jacobi-AMB performs well in efficiency; under certain circumstances, its stability and effectiveness also perform well.

中文翻译：

---

一种用于同步正交张量对角化的稀疏优化方法


该文提出了一种用于同步正交张量对角化的稀疏优化方法。该模型将张量的非对角线元素视为需要稀疏性的实体，由 l1 范数正则化器指导以优化对角化过程。该文提出一种基于梯度的交替多区组 Jacobi-AMB 算法来解决正交群乘积的优化问题。我们基于 Kurdyka-Łojasiewicz 属性建立全局收敛。数值实验表明，Jacobi-AMB 在效率方面表现良好;在某些情况下，它的稳定性和有效性也表现良好。