The use of grossone in elastic net regularization and sparse support vector machines

New algorithms for the numerical solution of optimization problems involving the l0 pseudo-norm are proposed. They are designed to use a recently proposed computational methodology that is able to deal numerically with finite, infinite and infinitesimal numbers. This new methodology introduces an infinite unit of measure expressed by the numeral ⃝1 (grossone) and indicating the number of elements of the set IN, of natural numbers. We show how the numerical system built upon ⃝1 and the proposed approximation of the l0 pseudo-norm in terms of ⃝1 can be successfully used in the solution of elastic net regularization problems and sparse support vector machines classification problems.