Solving LP using random projections

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• 作者：Leo Liberti ^{liberti@lix.polytechnique.fr" class="auth_mail" title="E-mail the corresponding author} ; Pierre-Louis Poirion ^{poirion@lix.polytechnique.fr" class="auth_mail" title="E-mail the corresponding author} ; Vu Khac Ky¹ ; ^{vu@lix.polytechnique.fr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Johnson-Lindenstrauss lemma ; random projection
• 刊名：Electronic Notes in Discrete Mathematics
• 出版年：2016
• 出版时间：November 2016
• 年：2016
• 卷：55
• 期：Complete
• 页码：53-56
• 全文大小：178 K

文摘

A celebrated result of Johnson and Lindenstrauss asserts that, in high enough dimensional spaces, Euclidean distances defined by a finite set of points are approximately preserved when these points are projected to a certain lower dimensional space. We show that the distance from a point to a convex set is another approximate invariant, and leverage this result to approximately solve linear programs with a logarithmic number of rows.