The concepts of infinity and infinitesimal in mathematics date back to
anciens Greek and have always attracted great attention. Very recently, a new
methodology has been proposed by Sergeyev for performing calculations with
infinite and infinitesimal quantities, by introducing an infinite unit of
measure expressed by the numeral grossone. An important characteristic of this
novel approach is its attention to numerical aspects. In this paper we will
present some possible applications and use of grossone in Operations Research
and Mathematical Programming. In particular, we will show how the use of
grossone can be beneficial in anti--cycling procedure for the well-known
simplex method for solving Linear Programming Problems and in defining exact
differentiable Penalty Functions in Nonlinear Programming
