Vertex Generation Methods for Problems with Logical Constraints

Recent work has shown how to use vertex generation methods to solve linear complementarity problems and cardinality constrained linear programs. These problems can be characterized as linear programs with additional logical constraints. These logical constraints can be incorporated into Chernikova's vertex generating algorithm in a natural and straightforward fashion. This study examines the extension of this technique to other linear programs with logical constraints, and discusses its use as a solution procedure for the 0–1 integer programming problem.