Exponential Decay of Sensitivity in Graph-Structured Nonlinear Programs
Name
21m1391079.pdf
Description
Published version
Size
1.85 MB
Format
Adobe PDF
Checksum (MD5)
18a3af349ede23ad5b145b84ef1c264d
Author(s)
Shin, Sungho
Anitescu, Mihai
Zavala, Victor M
Date Issued
June 2022
Journal
SIAM Journal on Optimization
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
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.
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/21M1391079
