Rescaling Algorithms for Linear Programming - Part I: Conic feasibility

@article{Dadush2016RescalingAF,
title={Rescaling Algorithms for Linear Programming - Part I: Conic feasibility},
author={Daniel Dadush and L{\'a}szl{\'o} A. V{\'e}gh and Giacomo Zambelli},
journal={CoRR},
year={2016},
volume={abs/1611.06427}
}

We propose simple polynomial-time algorithms for two linear conic feasibility problems. For a matrix A ∈ Rm×n, the kernel problem requires a positive vector in the kernel of A, and the image problem requires a positive vector in the image of A. Both algorithms iterate between simple first order steps and rescaling steps. These rescalings steps improve natural geometric potentials in the domain and image spaces, respectively. If Goffin’s condition measure ρ̂A is negative, then the kernel problem… CONTINUE READING