Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression

Orizon Ferreira; Yingchao Gao; Sandor Nemeth

doi:10.1080/02331934.2022.2103415

Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression

Orizon Ferreira, Yingchao Gao, Sandor Nemeth

Mathematics

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Abstract

This paper introduces the monotone extended second-order cone (MESOC), which is related to the monotone cone and the second-order cone. Some properties of the MESOC are presented and its dual cone is computed. Projecting onto the MESOC is reduced to the pool-adjacent-violators algorithm (PAVA) of isotonic regression. An application of MESOC to portfolio optimisation is provided. Some broad descriptions
of possible MESOC-regression models are also outlined.

Original language	English
Pages (from-to)	1-15
Number of pages	15
Journal	Optimization
Volume	2022
Early online date	21 Jul 2022
DOIs	https://doi.org/10.1080/02331934.2022.2103415
Publication status	E-pub ahead of print - 21 Jul 2022

Keywords

Extended second-order cone
dual cone
isotonic regression
metric projection

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Ferreira2022MonotonicallyAccepted author manuscript, 257 KBLicence: Creative Commons: Attribution-NonCommercial (CC BY-NC)

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AB - This paper introduces the monotone extended second-order cone (MESOC), which is related to the monotone cone and the second-order cone. Some properties of the MESOC are presented and its dual cone is computed. Projecting onto the MESOC is reduced to the pool-adjacent-violators algorithm (PAVA) of isotonic regression. An application of MESOC to portfolio optimisation is provided. Some broad descriptionsof possible MESOC-regression models are also outlined.

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ER -

Reducing the projection onto the monotone extended second-order cone to the pool-adjacent-violators algorithm of isotonic regression

Abstract

Keywords

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