Interior-point algorithms for a generalization of linear programming and weighted centring

@article{Anstreicher2012InteriorpointAF,
title={Interior-point algorithms for a generalization of linear programming and weighted centring},
author={Kurt M. Anstreicher},
journal={Optimization Methods and Software},
year={2012},
volume={27},
pages={605-612}
}

We consider an extension of ordinary linear programming (LP) that adds weighted logarithmic barrier terms for some variables. The resulting problem generalizes both LP and the problem of finding the weighted analytic center of a polytope. We show that the problem has a dual of the same form and give complexity results for several different interior-point algorithms. We obtain an improved complexity result for certain cases by utilyzing a combination of the volumetric and logarithmic barriers… CONTINUE READING