The tensor complementarity problem over circular cone (CCTCP for short) is studied, which is a specially structured nonlinear complementarity problem. Useful properties of the circular cone help to reformulate equivalently CCTCP as an implicit fixed-point equation. Based on the smoothing functions, we reformulate the obtained fixed-point equation as a family of parameterized smoothing equations. Moreover, we propose a modified Levenberg–Marquardt (LM) algorithm to solve the problem iteratively and show that the sequence generated by the new algorithm converges to a solution quadratically under suitable conditions. Preliminary numerical results demonstrate that the proposed algorithm is effective.

研究了圆锥上的张量互补问题（简称CCTCP），这是一个特殊结构的非线性互补问题。圆锥体的有用特性有助于将 CCTCP 等效地重新表述为隐式定点方程。基于平滑函数，我们将获得的不动点方程重新表述为参数化平滑方程族。此外，我们提出了一种改进的 Levenberg-Marquardt (LM) 算法来迭代解决问题，并表明新算法生成的序列在合适的条件下二次收敛到解。初步的数值结果表明所提出的算法是有效的。