Order isotonicity of the metric projection onto a closed convex cone

2016/02/15 by A. B. Németh, Németh, A. B., S. Z. Németh +1
Mathematics · #FOS: Mathematics #Optimization and Control (math.OC) #math.OC

paper · pdf · doi:10.48550/arxiv.1602.04743

11 pages

arxiv created 2016/02/15 · arxiv updated 2016/02/16

Abstract

The basic tool for solving problems in metric geometry and isotonic regression is the metric projection onto closed convex cones. Isotonicity of these projections with respect to a given order relation can facilitate finding the solutions of the above problems. In the recent note "A. B. Németh and S.Z. Németh: Isotonic regression and isotonic projection. Linear Algebra and its Applications, 494: 80-89 (2016)" this problem was studied for the coordinate-wise ordering. This study was the starting point for further investigations, such as the ones presented here. The order relation in the Euclidean space endowed by a proper cone is considered and the proper cones admitting isotone metric projections with respect to this order relation are investigated.

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