An algorithm for the nonlinear programming problem of the railway Yield Management

Abstract

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 define 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 differentiable merit function whose unconstrained 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 define descent search directions which are particularly well suited for the proposed merit..