A General Model of Some Inverse Combinatorial Optimization Problems and Its Solution Method Under l∞ Norm

Abstract

This paper proposes an optimization model and shows that most inverse combinatorial optimization problems so far discussed can be fit into this model as special cases. We propose a Newton-type algorithm for this model under l∞ norm. This algorithm can solve the model in strongly polynomial time if the subproblem involved is solvable in strongly polynomial time for any fixed value of the parameter appearing in the subproblem, and it is shown that most particular inverse optimization problems encountered are this kind. Therefore, through this paper we show that a large group of inverse optimization problems can be handled in a uniform way and solved in strongly polynomial time.