The analyticity of interior-point-paths at strictly complementary solutions of linear programs

Abstract

This paper investigates the analyticity of certain paths that arise in the context of feasible interior-point-methods. It is shown that there exists a neigborhood surrounding a strictly complementary optimal point where the path is analytic and all its derivatives with respect to the path parameter exist, even if the linear program is degenerate. For this reason it is possible to extend the path through the feasible region from the positive real axis to the left complex half plane. This is done by a canonical transformation of the linear program. The analyticity provides the theoretical foundation for numerical methods following the path by higher-order approximations