Multivariate adaptive regression spline (MARS) denotes a tool from statistics, important in classification and regression, with applicability in many areas of finance, science and technology. It is very useful in high dimensions and shows a great promise for fitting nonlinear multivariate functions. The MARS algorithm for estimating the model function consists of two subalgorithms. We propose not to use the second one (backward stepwise algorithm), but we construct a penalized residual sum of squares for a Tikhonov regularization problem which we treat using continuous optimization, considered to become a complementary technology and alternative to the backward stepwise algorithm. Especially, we employ conic quadratic programming (CQP), permitting the use of interior point methods.