Abstract
It has been an open question whether the family of merit functions ψ p ( p > 1 ) \psi _p\ (p>1) , the generalized Fischer-Burmeister (FB) merit function, associated to the second-order cone is smooth or not. In this paper we answer it partly, and show that ψ p \psi _p is smooth for p ∈ ( 1 , 4 ) p\in (1,4) , and we provide the condition for its coerciveness. Numerical results are reported to illustrate the influence of p p on the performance of the merit function method based on ψ p \psi _p .
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