Solvability of Newton equations in smoothing-type algorithms for the SOCCP
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摘要
In this paper, we first investigate the invertibility of a class of matrices. Based on the obtained results, we then discuss the solvability of Newton equations appearing in the smoothing-type algorithm for solving the second-order cone complementarity problem (SOCCP). A condition ensuring the solvability of such a system of Newton equations is given. In addition, our results also show that the assumption that the Jacobian matrix of the function involved in the SOCCP is a P0-matrix is not enough for ensuring the solvability of such a system of Newton equations, which is different from the one of smoothing-type algorithms for solving many traditional optimization problems in ℜn.
论文关键词:90C26,90C30,90C33,Solvability of Newton equations,Smoothing-type algorithm,Second-order cone complementarity problem
论文评审过程:Received 17 January 2010, Available online 26 October 2010.
论文官网地址:https://doi.org/10.1016/j.cam.2010.10.025