New mixed integer fractional programming problem and some multi-objective models for sparse optimization

We propose a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. We put special emphasis on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. We address the continuous relaxation of the problem, which comes out in the form of a fractional programming problem (FPP). In particular, we consider a possible way for tackling FPP by reformulating it via a DC (Difference of Convex) decomposition. We also overview the SVM models and the related Feature Selection in terms of multi-objective optimization. The results of some numerical experiments on benchmark classification datasets are reported.

Automated summary

This study proposes a novel Mixed-Integer Nonlinear Programming (MINLP) model for sparse optimization based on the polyhedral k-norm. The focus is specifically on the application of sparse optimization in Feature Selection for Support Vector Machine (SVM) classification. The study addresses the continuous relaxation problem through reformulation via DC (Difference of Convex) decomposition. Additionally, it provides an overview of SVM models and related Feature Selection in terms of multi-objective optimization, and reports the results of numerical experiments on benchmark classification datasets.