Generalized-Hukuhara Subgradient Method for Optimization Problem with Interval-valued Functions and its Application in Lasso Problem

TL;DR

This paper introduces a $gH$-subgradient method for efficiently solving optimization problems involving nonsmooth convex interval-valued functions, demonstrated through an application to interval-valued feature lasso regression.

Contribution

It develops a novel $gH$-subgradient technique for nonsmooth convex interval-valued functions and applies it to interval-valued feature lasso regression.

Findings

Efficient solutions for nonsmooth convex interval-valued optimization problems.

Application to interval-valued feature lasso regression demonstrates practical utility.

Algorithmic implementation of the $gH$-subgradient technique is provided.

Abstract

In this study, a \emph{$gH$-subgradient technique} is developed to obtain efficient solutions to the optimization problems with nonsmooth nonlinear convex interval-valued functions. The algorithmic implementation of the developed $gH$-subgradient technique is illustrated. As an application of the proposed \emph{$gH$-subgradient technique}, an $\ell_1$ penalized linear regression problem, known as a \emph{lasso problem}, with interval-valued features is solved.