A Penalty-Function Approach to a Mixed-Integer Bilevel Programming Problem

Abstract: In this paper, we present a mathematical framework for the problem of minimizing the cash-out penalties from the point of view of the natural gas shipper. The problem is modeled as a mixed bilevel linear programming problem. To solve it efficiently, we reformulate it as a standard mathematical programming problem and describe an algorithm of penalty functions for its solution. The algorithm is well-founded and its convergence is proved.