A New Generalized FB Complementarity Function for Symmetric Cone Complementarity Problems (Communications in Mathematical Research, 2021)
We establish that the generalized Fischer-Burmeister (FB) function andpenalized Generalized Fischer-Burmeister (FB) function defined on symmetric conesare complementarity functions (C-functions), in terms of Euclidean Jordan algebras,and the Generalized Fischer-Burmeister complementarity function for the symmetriccone complementarity problem (SCCP). It provides an affirmative answer to the openquestion by Kum and Lim (Kum S H, Lim Y. Penalized complementarity functionson symmetric cones. $J$. $Glob$. $Optim$.. 2010, 46: 475–485) for any positive integer.
Keywords: complementarity problem; complementarity function; symmetric cone; generalized Fischer-Burmeister function.