  We propose a framework for sensitivity analysis of linear programs (LPs) in
minimization form, allowing for simultaneous perturbations in the objective
coefficients and right-hand sides, where the perturbations are modeled in a
compact, convex uncertainty set. This framework unifies and extends multiple
approaches for LP sensitivity analysis in the literature and has close ties to
worst-case linear optimization and two-stage adaptive optimization. We define
the minimum (best-case) and maximum (worst-case) LP optimal values, p- and p+,
over the uncertainty set, and we discuss issues of finiteness, attainability,
and computational complexity. While p- and p+ are difficult to compute in
general, we prove that they equal the optimal values of two separate, but
related, copositive programs. We then develop tight, tractable conic
relaxations to provide lower and upper bounds on p- and p+, respectively. We
also develop techniques to assess the quality of the bounds, and we validate
our approach computationally on several examples from--and inspired by--the
literature. We find that the bounds on p- and p+ are very strong in practice
and, in particular, are at least as strong as known results for specific cases
from the literature.
