Saddle Points and Pareto Points in Multiple Objective Programming

In this paper relationships between Pareto points and saddle points in multiple objective programming are investigated. Convex and nonconvex problems are considered and the equivalence between Pareto points and saddle points is proved in both cases. The results are based on scalarizations of multiple objective programs and related linear and augmented Lagrangian functions. Partitions of the index sets of objectives and constraints are introduced to reduce the size of the problems. The relevance of the results in the context of decision making is also discussed.