This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈Q.If we simpl...This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈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.展开更多
基金the National Natural Science Foundation of China(Nos.11101028 and 11271206)National Key R&D Program of China(No.2017YFF0207401)the Fundamental Research Funds for the Central Universities(No.FRF-DF-19-004).
文摘This paper considers the tensor split feasibility problem.Let C and Q be non-empty closed convex set and A be a semi-symmetric tensor.The tensor split feasibility problem is to find x∈C such that Axm−1∈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.
