A common goal throughout science and engineering is to solve optimization
problems constrained by computational models. However, in many cases a
high-fidelity numerical emulation of systems cannot be optimized due to code
complexity and computational costs which prohibit the use of intrusive and many
query algorithms. Rather, lower-fidelity models are constructed to enable
intrusive algorithms for large-scale optimization. As a result of the
discrepancy between high and low-fidelity models, optimal solutions determined
using low-fidelity models are frequently far from true optimality. In this
article we introduce a novel approach that uses post-optimality sensitivities
with respect to model discrepancy to update the optimization solution. Limited
high-fidelity data is used to calibrate the model discrepancy in a Bayesian
framework which in turn is propagated through post-optimality sensitivities of
the low-fidelity optimization problem. Our formulation exploits structure in
the post-optimality sensitivity operator to achieve computational scalability.
Numerical results demonstrate how an optimal solution computed using a
low-fidelity model may be significantly improved with limited evaluations of a
high-fidelity model