Geodesic Convexity on R + n

Abstract

Many of the numerous articles published recently on interior point algorithms focused on vector fields, potential functions and the analysis of the potential reduction methods. Affine and projective scaling methods based on the affine and projective vector fields are originated from affine and projective metrics. Riemannian geometry underlying interior point methods was investigated in Karmarkar (1990), the affine and projective scaling trajectories in Bayer and Lagarias (1989/a, 1989/b) and the integrability of vector and multivector fields associated with interior point methods in Iri (1991).