Monotonicity of Primal and Dual Objective Values in Primal-dual Interior-point Algorithms

We study monotonicity of primal and dual objective values in the framework of primal-dual interior-point methods. The primal-dual aane-scaling algorithm is monotone in both objectives. We derive a condition under which a primal-dualinterior-point algorithm with a centering component is monotone. Then we propose primal-dual algorithms that are monotone in both primal and dual objective values and achieve polynomial time bounds. We also provide some arguments showing that several existing primal-dual algorithms use parameters close to one that almost always improves both objectives.