Finding all solution sets of piecewise-linear interval equations using integer programming

This paper presents an efficient method for finding all solution sets of piecewise-linear interval equations using integer programming. In this method, the problem of finding all solution sets is formulated as a mixed integer programming problem, and it is solved by a high-performance integer programming solver such as CPLEX. It is shown that the proposed method can be implemented easily without writing complicated programs, and that all solution sets are obtained by solving a mixed integer programming problem only once. Numerical examples are given to confirm the effectiveness of the proposed method.