This paper discusses how to compute all real solutions of the second-order cone tensor complementarity problem when there are finitely many ones. For this goal, we first formulate the second-order cone tensor complementarity problem as two polynomial optimization problems. Based on the reformulation, a semidefinite relaxation method is proposed by solving a finite number of semidefinite relaxations with some assumptions. Numerical experiments are given to show the efficiency of the method.

中文翻译：

---

二阶锥多项式互补问题的半定松弛方法

本文讨论了在有限数量的情况下如何计算二阶锥张量互补问题的所有实解。为此，我们首先将二阶锥张量互补问题表述为两个多项式优化问题。在重新设计的基础上，通过一些假设，解决有限数量的半定松弛，提出一种半定松弛方法。数值实验表明了该方法的有效性。