A Proof of Sparseness, Optimality, and Convergence of an LP-SVR

This article presents a proof of convergence and sparsity of a linear programming support vector machine for regression. First, the Support Vector Regression (SVR) problem is posed as a linear programming problem modeled on a primal and dual fashion leading to the definitions of optimality. Second, we describe a sequential optimization method based on variables decomposition, constraints decomposition, and primal-dual interior point methods for solving large-scale regression/classification problems. Third, based on the methodology, we present proof of convergence and optimality conditions of the sequential optimization and its ability to produce sparse solutions.