
Journal of Convex Analysis 29 (2022), No. 3, 827836 Copyright Heldermann Verlag 2022 A Convex Analysis View of the Barrier Problem Mihály Bessenyei Institute of Mathematics, University of Debrecen, Hungary besse@science.unideb.hu Norbert Tóth Institute of Mathematics, University of Debrecen, Hungary tothnor97@gmail.com Besides the simplex algorithm, linear programs can also be solved via interior point methods. The theoretical background of such algorithms is the classical logbarrier problem. The aim of this note is to study and generalize the barrier problem using the standard tools of Convex Analysis. Keywords: Logbarrier problem, Lagrange multipliers, complementary slackness, recessional cone. MSC: 90C51; 52A41, 90C05, 90C25. [ Fulltextpdf (171 KB)] for subscribers only. 