A Levenberg–Marquardt Method for Solving the Tensor Split Feasibility Problem

Abstract

This paper considers the tensor split feasibility problem. Let C and Q be non-empty closed convex set and $${\mathcal {A}}$$ be a semi-symmetric tensor. The tensor split feasibility problem is to find $$x\in C $$ such that $${\mathcal {A}} x^{m-1} \in Q$$ . If we simply take this problem as a special case of the nonlinear split feasibility problem, then we can directly get a projection method to solve it. However, applying this kind of projection method to solve the tensor split feasibility problem is not so efficient. So we propose a Levenberg–Marquardt method to achieve higher efficiency. Theoretical analyses are conducted, and some preliminary numerical results show that the Levenberg–Marquardt method has advantage over the common projection method.