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arXiv · 0807.4053

A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming

Yoshio Uwano·Hiromi Yuya
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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.

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Yoshio Uwano, Hiromi Yuya. 2008-07-25. A gradient system on the quantum information space that realizes the Karmarkar flow for linear programming. https://arxiv.org/abs/0807.4053

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