In this paper we investigate the asymptotic stability of dynamic, multiple-objective linear programs. In particular, we show that a generalization of the optimal partition stabilizes for a large class of data functions. This result is based on a new theorem about asymptotic sign-solvable systems. The stability properties of the generalized optimal partition are used to extend a dynamic version of the Nonsubstitution Theorem.
Cayton, L., Herring, R., Holder, A., Holzer, J., Nightingale, C., & Stohs, T. (2006). Asymptotic sign-solvability, multiple objective linear programming, and the nonsubstitution theorem. Mathematical Methods of Operations Research, 64(3), 541-555. doi:10.1007/s00186-006-0095-z
Mathematical Methods of Operations Research