Linear Classification of data with Support Vector Machines and Generalized Support Vector Machines

TL;DR

This paper explores support vector machines and introduces generalized support vector machines, linking them to variational inequalities and providing theoretical results and examples for their solutions.

Contribution

It introduces the concept of generalized support vector machines and establishes their connection to variational inequalities, expanding the theoretical framework.

Findings

Generalized support vector machines are equivalent to generalized variational inequalities.

Existence of solutions for generalized support vector machines is established.

Examples support the theoretical results.

Abstract

In this paper, we study the support vector machine and introduced the notion of generalized support vector machine for classification of data. We show that the problem of generalized support vector machine is equivalent to the problem of generalized variational inequality and establish various results for the existence of solutions. Moreover, we provide various examples to support our results.