Journal of Convex Analysis 29 (2022), No. 3, 827--836
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 log-barrier problem. The aim of this note is to study and generalize the barrier problem using the standard tools of Convex Analysis.
Keywords: Log-barrier problem, Lagrange multipliers, complementary slackness, recessional cone.
MSC: 90C51; 52A41, 90C05, 90C25.
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