张量特征值互补问题因其在多项式优化问题中的广泛应用而引起人们的高度关注。本项目主要针对二阶锥上的张量特征值互补问题进行研究，内容包括：利用二阶锥的结构揭示张量Lorentz谱的上下界性质和结构特征；通过投影技术建立二阶锥上张量特征值互补问题的易于求解的新模型，建立不动点算法；利用欧几里得若当代数，结合枚举法和光滑型算法，建立求解二阶锥上一般张量特征值互补问题的混合优化算法；对所建立的算法进行适定性和收敛性分析，并利用数值试验检验算法效果。此项目的成功实施将深刻揭示张量Lorentz谱的结构特征和性质，为求解张量特征值互补问题提供两类新的有效的鲁棒算法。

Tensor eigenvalue complementarity problem receives much attention of researchers due to its wide applications in polynomial optimization problem. This project focus on the tensor eigenvalue complementarity problem associated with second-order cone. The main objective includes revealing the bounded property and the structure characters of Lorentz spectrum for tensors by the structure of the second-order cone; establishing an easily tractable optimization models and a fixed point algorithm of the tensor eigenvalue complementarity problem associated with the second-order cone via projection techniques; proposing a “enumerative - smoothing” hybrid algorithm for general tensor eigenvalue complementarity problem associated with the second-order cone by using of the Euclidean Jordan algebra; discussing the well-definedness and the convergence and making numerical experiments for the proposed algorithms. The success of this project will reveal the characters and the properties of Lorentz spectrum for tensors and provide two classes of new efficient robust algorithms for the tensor eigenvalue complementarity problem.