Given a (combinatorial) optimization problem and a feasible solution to it, the corresponding inverse optimization problem is to find a minimal adjustment of the cost function such that the given solution becomes optimum. Several such problems have been studied in the last ten years. After formalizing the notion of an inverse problem and its variants, we present various methods for solving them. Then we discuss the problems considered in the literature and the results that have been obtained. Finally, we formulate some open problems.
Heuberger REF provides an excellent survey of the diverse inverse optimization problems that have been tackled.
Inverse Combinatorial Optimization: A Survey on Problems, Methods, and Results
TO APPEAR IN JOURNAL OF COMBINATORIAL OPTIMIZATION
Mathematics Computer Science