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arXiv · 2304.00244

An active-set based recursive approach for solving convex isotonic regression with generalized order restrictions

Xuyu Chen·Xudong Li·Yangfeng Su
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Abstract

This paper studies the convex isotonic regression with generalized order restrictions induced by a directed tree. The proposed model covers various intriguing optimization problems with shape or order restrictions, including the generalized nearly isotonic optimization and the total variation on a tree. Inspired by the success of the pool-adjacent-violator algorithm and its active-set interpretation, we propose an active-set based recursive approach for solving the underlying model. Unlike the brute-force approach that traverses an exponential number of possible active-set combinations, our algorithm has a polynomial time computational complexity under mild assumptions.

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Xuyu Chen, Xudong Li, Yangfeng Su. 2023-04-01. An active-set based recursive approach for solving convex isotonic regression with generalized order restrictions. https://arxiv.org/abs/2304.00244

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