论文标题
多线性方程的稀疏最小二乘解决方案
Sparse least squares solutions of multilinear equations
论文作者
论文摘要
在本文中，我们提出了一个稀疏的最小二乘（SLS）优化模型，用于求解多线性方程，其中对解决方案的稀疏性约束可以有效地降低存储和计算成本。通过采用稀疏集的变分特性，以及SLS模型中目标函数的分化特性，可以根据固定点进行一阶最佳条件。根据固定点的等效表征，我们提出了牛顿硬阈值追求（NHTP）算法，并在某些规律条件下建立其本地二次收敛。在模拟数据集上进行的数值实验，包括完全正（CP）量表和对称强度M量的病例，说明了我们提出的NHTP方法的功效。
In this paper, we propose a sparse least squares (SLS) optimization model for solving multilinear equations, in which the sparsity constraint on the solutions can effectively reduce storage and computation costs. By employing variational properties of the sparsity set, along with differentiation properties of the objective function in the SLS model, the first-order optimality conditions are analyzed in terms of the stationary points. Based on the equivalent characterization of the stationary points, we propose the Newton Hard-Threshold Pursuit (NHTP) algorithm and establish its locally quadratic convergence under some regularity conditions. Numerical experiments conducted on simulated datasets including cases of Completely Positive(CP)-tensors and symmetric strong M-tensors illustrate the efficacy of our proposed NHTP method.
