optimization problem

flying

Hi, I have an optimization problem using tensor representation.



[tex] max_b A \times_1 b \times_2 b \times_3 b [/tex]
[tex] s.t. b^T b = 1 [/tex]

where [tex] A [/tex] is an [tex] n \times n \times n [/tex] tensor. [tex] b [/tex] is an [tex] n \times 1 [/tex] vector. In the 2D case, I know the solution to [tex] b[/tex] is the eigenvector corresponding to the maximum eigenvalue of [tex] A [/tex]. Is there any similar property in the 3D case?

thanks!