Tensor complementarity problem (TCP) has attracted many attentions in recent years. In this paper, we equivalently reformulate tensor complementarity problem as a fixed point equation. Based on the fixed point equation, projected fixed point iterative methods are proposed and corresponding convergence proofs on the fixed point iterative methods for the tensor complementarity problem associated with a power Lipschitz tensor are investigated. Furthermore, the monotone convergence analysis of the fixed point iteration method for the tensor complementarity problem involving an \({\mathcal {L}}\) tensor is given. Numerical examples are tested to illustrate the given approach.

近年来，张量互补问题（TCP）引起了很多关注。在本文中，我们将张量互补问题等效地重新定为不动点方程。基于不动点方程，提出了投影不动点迭代方法，研究了与幂立普兹茨张量相关的张量互补问题的不动点迭代方法的对应收敛性证明。此外，给出了涉及一个\（{{mathcal {L}} \）张量的张量互补问题的不动点迭代方法的单调收敛性分析。测试了数值示例以说明给定的方法。