Abstract
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.
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