Penalized Generalized Fischer-Burmeister Function for Soccp

Abstract

Recently, Pan et al. [11] developed the merit function method for SOCCP based on the generalized Fischer-Burmeister (FB) function. This note is along the same line. Indeed, we study a penalized version of the generalized FB function and provide a basic theoretical property that the level set of the merit function induced by the penalized version of the generalized FB function is bounded under suitable assumptions. The proof relies on trace inequalities.