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A smoothing Newton method for second-order cone optimization based on a new smoothing function. (English) Zbl 1229.65101
Summary: A new smoothing function is given by smoothing the symmetric perturbed Fischer-Burmeister function. Based on this new smoothing function, we present a smoothing Newton method for solving the second-order cone optimization (SOCO). The method solves only one linear system of equations and performs only one line search at each iteration. Without requiring strict complementarity assumption at the SOCO solution, the proposed algorithm is shown to be globally and locally quadratically convergent. Numerical results demonstrate that our algorithm is promising and comparable to interior-point methods.

65K05 Numerical mathematical programming methods
90C25 Convex programming
90C53 Methods of quasi-Newton type
90C51 Interior-point methods
Full Text: DOI
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