This issuePrevious ArticleGlobal existence for a functional reaction-diffusion problem from climate modelingNext ArticleOn general Sturmian theory for abnormal linear Hamiltonian systems
Modern interior-point methods used for optimization on convex
sets in ane space are based on the notion of a barrier function. Projective
space lacks crucial properties inherent to ane space, and the concept of a
barrier function cannot be directly carried over. We present a self-contained
theory of barriers on convex sets in projective space which is build upon the
projective cross-ratio. Such a projective barrier equips the set with a Codazzi
structure, which is a generalization of the Hessian structure induced by a barrier
in the ane case. The results provide a new interpretation of the ane theory
and serve as a base for constructing a theory of interior-point methods for
projective convex optimization.