# Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs

@article{Shin2022ExponentialDO, title={Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs}, author={Sungho Shin and Mihai Anitescu and Victor M. Zavala}, journal={SIAM J. Optim.}, year={2022}, volume={32}, pages={1156-1183} }

We study solution sensitivity for nonlinear programs (NLPs) whose structure is induced by a graph $\mathcal{G}=(\mathcal{V},\mathcal{E})$. These graph-structured NLPs arise in many applications such as dynamic optimization, stochastic optimization, optimization with partial differential equations, and network optimization. We show that the sensitivity of the primal-dual solution at node $i\in \mathcal{V}$ against a data perturbation at node $j\in \mathcal{V}$ is bounded by $\Upsilon \rho^{d_…

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