This paper provides sufficient conditions for the optimal value function of a given linear semi-infinite programming problem to depend linearly on the size of the perturbations, when these perturbations are directional, involve either the cost coefficients or the right-hand-side function or both, and they are sufficiently small. Two kinds of partitions are considered. The first one concerns the effective domain of the optimal value as a function of the cost coefficients, and consists of maximal regions on which this value function is linear. The second class of partitions considered in the paper concern the index set of the constraints through a suitable extension of the concept of optimal partition from ordinary to semi-infinte linear programming. These partitions provide convex sets, in particular segments, on which the optimal value is a linear function of the size of the perturbations, for the three types of perturbations considered in this paper.
Report AdvOL 2006/14, Advanced Optimization Lab., McMaster University, December 2006. http://optlab.mcmaster.ca/