Rapid heuristic projection on simplicial cones

A. Ekárt, A. Nemeth, S. Nemeth

Research output: Working paper

Abstract

A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.
Original languageEnglish
Publication statusPublished - 12 Jan 2010

Fingerprint

Cone
Projection
Heuristics
Iteration
Heuristic Method
Percent
Higher Dimensions
Exact Solution
Linear Systems
Decrease
Experiment

Bibliographical note

© 2010 The Authors

Keywords

  • math.OC

Cite this

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Rapid heuristic projection on simplicial cones. / Ekárt, A.; Nemeth, A.; Nemeth, S.

2010.

Research output: Working paper

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AU - Nemeth, S.

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N2 - A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

AB - A very fast heuristic iterative method of projection on simplicial cones is presented. It consists in solving two linear systems at each step of the iteration. The extensive experiments indicate that the method furnishes the exact solution in more then 99.7 percent of the cases. The average number of steps is 5.67 (we have not found any examples which required more than 13 steps) and the relative number of steps with respect to the dimension decreases dramatically. Roughly speaking, for high enough dimensions the absolute number of steps is independent of the dimension.

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UR - https://arxiv.org/abs/1001.1928

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Ekárt A, Nemeth A, Nemeth S. Rapid heuristic projection on simplicial cones. 2010 Jan 12.