Parametric analysis of conic linear optimization

This paper focuses on the parametric analysis of a conic linear optimization problem with respect to the perturbation of the objective function along many fixed directions. We introduce the concept of the primal and dual conic linear inequality representable sets, which is very helpful for converting the correlation of the parametric conic linear optimization problems into the set-valued mapping relation. We discuss the relationships between these two sets and present the invariant region decomposition of a conic linear inequality representable set. We study the behaviour of the optimal partition and investigate the sensitivity of the optimal partition for conic linear optimization problems. All results are corroborated by examples having correlation among parameters.