Abstract
We present a new one-parametric class of smoothing functions for second-order cone programming (denoted by SOCP). This class is fairly general and includes the well-known Fischer–Burmeister smoothing function and the Chi–Liu smoothing function (J Comput Appl Math 223:114–123, 2009) as special cases. Based on these functions, a smoothing-type method is proposed for solving SOCP. The proposed algorithm solves only one linear system of equations and performs only one line search at each iteration. This algorithm can start from an arbitrary point and it is locally superlinearly convergent under a mild assumption. Some numerical results are reported.
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