求解张量分裂可行问题的半定松弛法

Semidefinite Relaxation Algorithm for Solving Tensor Split Feasibility Problem

投影法是求解分裂可行问题的传统方法,但投影法的求解效率依赖于初始点的选择,且无法直接应用于张量分裂可行问题。本文提出了利用半定松弛法来求解一类特殊的张量分裂可行问题。假设问题中集合的形式由多项式不等式给出,则可将张量分裂可行问题松弛化为半定规划问题,再应用半定松弛法求解。本文给出了半定松弛法的相关原理,并进行了数值实验。实验结果表明:对于集合取不同范围、张量中的元素取不同值、张量取不同维数和不同阶数,该松弛化方法都能够用于求解张量分裂可行问题。

Projection method was a traditional method for solving split feasibility problem.However,the solving efficiency of projection method depended on the selection of initial point and it was not directly applied to solve the tensor split feasibility problem. A new idea by using semidefinite relaxation algorithm to solve a kind of specific tensor split feasibility problem was proposed.The form of sets was given by polynomials inequalities,so the tensor split feasibility problem was relaxed to semidefinite program problem. The semidefinite relaxation method was used to solve the problem. The correlation theory of the semidefinite relaxation method was given and numerical experiments were carried out. The experimental results show that for different ranges of sets,different element values of tensors,different dimensions and different orders of tensors,the relaxation method can be used to solve the tensor split feasibility problem.