The data describing an asymptotic linear program rely on a single parameter, usually referred to as time, and unlike parametric linear programming, asymptotic linear programming is concerned with the steady state behavior as time increases to infinity. The fundamental result of this work shows that the optimal partition for an asymptotic linear program attains a steady state for a large class of functions. Consequently, this allows us to define an asymptotic center solution. We show that this solution inherits the analytic properties of the functions used to describe the feasible region. Moreover, our results allow significant extensions of an economics result known as the Nonsubstitution Theorem.
Hasfura-Buenaga, J.-R., Holder, A., & Stuart, J. (2005). The asymptotic optimal partition and extensions of the nonsubstitution theorem. Linear Algebra and Its Applications, 394, 145-167. doi:10.1016/j.laa.2004.05.018
Linear Algebra and its Applications