The SC1 property of the squared norm of the SOC Fischer-Burmeister function

Authors:
Jein-Shan Chen;Defeng Sun;Jie Sun
Affiliations:
Department of Mathematics, National Taiwan Normal University, Taipei, 11677, Taiwan;Department of Mathematics, National University of Singapore, Singapore 117543, Singapore;Department of Decision Sciences, National University of Singapore, Singapore 117592, Singapore
Venue:
Operations Research Letters
Year:
2008

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Abstract

We show that the gradient mapping of the squared norm of Fischer-Burmeister function is globally Lipschitz continuous and semismooth, which provides a theoretical basis for solving nonlinear second-order cone complementarity problems via the conjugate gradient method and the semismooth Newton's method.