An Algorithm for the Nonlinear Programming Problem of the Railway Yield Management

In this paper we consider the problem of solving a special class of nonlinear constrained optimization problems. The study of this class of problems has been motivated by a practical application, namely the railway yield management problem. The aim of this paper is to deene a nonlinear minimization algorithm which exploits as much as possible the structure of the problems under consideration. The approach followed is to transform the original constrained problem into the unconstrained minimization of a continuously diierentiable merit function whose un-constrained minimizers give a solution of the original constrained problem. In comparison with the merit functions proposed before in the literature, this new merit function has the distinguishing feature of taking full advantage of the particular structure of the constraints of the original problem. Furthermore we show also that it is possible to deene descent search directions which are particularly well suited for the proposed merit function. By using the new merit function and the related search directions it is possible to deene a class of globally and superlinearly convergent constrained minimization algorithms. We report also the results of a numerical experimentation performed by a preliminary implementation of an algorithm in this class. These results indicate that the proposed approach seems to be very promising.