A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming
Dynamical Systems
2010-10-27 v1 Mathematical Physics
math.MP
Abstract
In the paper of Uwano [Czech. J. of Phys., vol.56, pp.1311-1316 (2006)], a gradient system is found on the space of density matrices endowed with the quantum SLD Fisher metric (to be referred to as the quantum information space) that realizes a generalization of a gradient system on the space of multinomial distributions studied by Nakamura [Japan J. Indust. Appl. Math., vol.10, pp.179-189 (1993)]. On motived by those papers, the present paper aims to construct a gradient system on the quantum information space that realizes the Karmarkar flow, the continuous limit of the Karmarkar projective scaling algorithm for linear programming.
Cite
@article{arxiv.0807.4053,
title = {A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming},
author = {Yoshio Uwano and Hiromi Yuya},
journal= {arXiv preprint arXiv:0807.4053},
year = {2010}
}