  We study solution sensitivity for nonlinear programs (NLPs) whose structures
are induced by graphs. These NLPs arise in many applications such as dynamic
optimization, stochastic optimization, optimization with partial differential
equations, and network optimization. We show that for a given pair of nodes,
the sensitivity of the primal-dual solution at one node against a data
perturbation at the other node decays exponentially with respect to the
distance between these two nodes on the graph. In other words, the solution
sensitivity decays as one moves away from the perturbation point. This result,
which we call exponential decay of sensitivity, holds under the strong
second-order sufficiency condition and the linear independence constraint
qualification. We also present conditions under which the decay rate remains
uniformly bounded; this allows us to characterize the sensitivity behavior of
NLPs defined over subgraphs of infinite graphs. The theoretical developments
are illustrated with numerical examples.
