A smoothing Newton method for second-order cone optimization based on a new smoothing function

A smoothing Newton method for second-order cone optimization based on a new smoothing function

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Article ID: iaor20118908
Volume: 218
Issue: 4
Start Page Number: 1317
End Page Number: 1329
Publication Date: Oct 2011
Journal: Applied Mathematics and Computation
Authors: , , ,
Keywords: heuristics
Abstract:

A new smoothing function is given in this paper 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.

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