The use of grossone in Mathematical Programming and Operations Research - De Cosmis, Sonia; De Leone, Renato (Applied mathematics and computation, 2012)
The concepts of infinity and infinitesimal in mathematics date back to ancients Greek and have always attracted great attention. Very recently, a new methodology has been proposed by Sergeyev [10] for performing calculations with infinite and infinitesimal quantities, by introducing an infinite unit of measure expressed by the numeral ① (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 ① in Operations Research and Mathematical Programming. In particular, we will show how the use of ① 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.