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

Abstract

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.

Multi-Objective Models for Sparse Optimization in Linear Support Vector Machine Classification

“…Our primary purpose is to demonstrate the advantages of considering these single-objective models as MOP models. In multi-objective form, we can obtain a set of Pareto-optimal solutions instead of an optimal solution in a single-objective form [58][59][60][61], and then the decision maker can choose one of these solutions [58][59][60].…”

“…Additionally, based on k-norm the following problem proposed in [58][59][60] for Sparse Optimization:…”