求解超对称张量秩-1逼近的BFGS方法

The BFGS method for solving the rank-1 approximation problem of supersymmetric tensors

为了解决超对称张量秩-1逼近问题,利用对称张量的结构特征和相关的矩阵理论,将该问题转化为等价的无约束优化问题,给出无约束优化问题的梯度表达式并证明,再设计BFGS方法进行求解。数值实验验证了方法的可行性。

In order to solve the rank-1 approximation problem of supersymmetric tensors.By making use of symmetric tensor structure features and related matrix theory,the problem is transformed into an equivalent unconstrained optimization problem.Then the gradient expression of unconstrained optimization problem is given and proved.The BFGS method is designed to solve the equivalent problem.Finally,numerical experiments show that this method is feasible.