Duality for nonlinear multiple-criteria optimization problems

In this paper, we develop a duality theory for nonlinear multiple-criteria optimization problems. The theory associates to efficient points a matrix, rather than a vector, of dual variables. We introduce a saddle-point dual problem, study stability concepts and Kuhn-Tucker conditions, and provide an economic interpretation of the dual matrix. The results are compared to the classical approach of deriving duality, by applying nonlinear programming duality theory to a problem obtained by conveniently weighting the criteria. Possible directions for future research are discussed.This work was performed under Grant No. MCS-77-24654, National Science Foundation.The author is grateful to Professors S. C. Graves and T. L. Magnanti, and two anonymous referees for helpful comments on an earlier version of this paper.