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Lipschitz continuity of the gradient of a one-parametric class of SOC merit functions
Abstract:In this article, we show that a one-parametric class of SOC merit functions has a Lipschitz continuous gradient; and moreover, the Lipschitz constant is related to the parameter in this class of SOC merit functions. This fact will lay a building block when the merit function approach as well as the Newton-type method are employed for solving the second-order cone complementarity problem with this class of merit functions.
Keywords:second-order cone  merit function  spectral factorization  Lipschitz continuity
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