A theorem of the alternative for multihomogeneous functions and its relationship to diagonal scaling of matrices
It is proved that given a multihomogeneous function satisfying some initial conditions, either it has a certain nonnegative zero over a given subspace, or an associated logarithmic barrier function has a constrained stationary point. Under convexity precisely one of these conditions is satisfied. The derivation of significant properties of the constrained stationary points of the logarithmic barrier function and their relationship to corresponding points of an associated Karmarkar potential function play an important role. The author being from computer science department, could have brought out some numerical applications.
scientific article; zbMATH DE number 871253
scientific article