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

TL;DR

This paper introduces the monotone extended second-order cone (MESOC), explores its properties, and demonstrates how projection onto MESOC can be efficiently performed using the pool-adjacent-violators algorithm, with applications in portfolio optimization.

Contribution

It defines the MESOC, analyzes its properties, and reduces projection onto it to PAVA, enabling efficient isotonic regression with new applications.

Findings

Projection onto MESOC reduces to PAVA.

Properties and dual cone of MESOC are characterized.

Application to portfolio optimization demonstrated.

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.