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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