2007 , Volume 12, № 2, p.3-22

Additive models belong to the techniques of modern statistical learning; they are applicable in many areas of prediction such as financial mathematics, computational biology, medicine, chemistry and environmental protection. They are fitted through backfitting algorithm using the \textit{partials residuals} proposed by \textit{Friedman and Stuetzle} (1981) [9]. In this paper, we firstly give an introduction and review. Then, we present a mathematical modeling by splines based on a new clustering approach for the input data $x$, their density, and the variation of the output data $y$. We contribute to regression with additive models by bounding (penalizing) second order terms (curvature) of the splines, leading to a more robust approximation. Now, we propose a refining modification and investigation of the \textit{backfitting algorithm} previously applied to additive models. By using the language of optimization theory, especially, conic quadratic programming, we initiate future research on and practical applications of solution methods with mathematical programming.