In this paper, we study the generalized subdifferentials and the Riemannian gradient subconsistency that are the basis for non-Lipschitz optimization on embedded submanifolds of [Formula: see text]. We then propose a Riemannian smoothing steepest descent method for non-Lipschitz optimization on complete embedded submanifolds of [Formula: see text]. We prove that any accumulation point of the sequence generated by the Riemannian smoothing steepest descent method is a stationary point associated with the smoothing function employed in the method, which is necessary for the local optimality of the original non-Lipschitz problem. We also prove that any accumulation point of the sequence generated by our method that satisfies the Riemannian gradient subconsistency is a limiting stationary point of the original non-Lipschitz problem. Numerical experiments are conducted to demonstrate the advantages of Riemannian [Formula: see text] [Formula: see text] optimization over Riemannian [Formula: see text] optimization for finding sparse solutions and the effectiveness of the proposed method. Funding: C. Zhang was supported in part by the National Natural Science Foundation of China [Grant 12171027] and the Natural Science Foundation of Beijing [Grant 1202021]. X. Chen was supported in part by the Hong Kong Research Council [Grant PolyU15300219]. S. Ma was supported in part by the National Science Foundation [Grants DMS-2243650 and CCF-2308597], the UC Davis Center for Data Science and Artificial Intelligence Research Innovative Data Science Seed Funding Program, and a startup fund from Rice University.
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Modeling the Impact of Community First Responders
In community first responder (CFR) systems, traditional emergency service response is augmented by a network of trained volunteers who are dispatched via an app. A central application of such systems is out-of-hospital cardiac arrest (OHCA), where a very fast response is crucial. For a target performance level, how many volunteers are needed, and from which locations should they be recruited? We model the presence of volunteers throughout a region as a Poisson point process, which permits the computation of the response-time distribution of the first-arriving volunteer. Combining this with known survival-rate functions, we deduce survival probabilities in the cardiac arrest setting. We then use convex optimization to compute a location distribution of volunteers across the region that optimizes either the fraction of incidents with a fast response (a common measure in the industry) or patient survival in the case of OHCA. The optimal location distribution provides a bound on the best possible performance with a given number of volunteers. This can be used to determine whether introducing a CFR system in a new region is worthwhile or can serve as a guide for additional recruitment in existing systems. Effective target areas for recruitment are not always obvious because volunteers recruited from one area may be found in various areas across the city depending on the time of day; we explicitly capture this issue. We demonstrate these methods through an extended case study of Auckland, New Zealand. This paper was accepted by Carri Chan, healthcare management. Funding: This research was financed in part by the Netherlands Organization for Scientific Research (NWO) in the form of a Rubicon grant (019.172EN.016) to C. J. Jagtenberg and a Veni grant (VI.Veni.191E.005) to P. L. van den Berg. S. G. Henderson and H. Li were supported in part by National Science Foundation [Grant CMMI-2035086]. Vrije Universiteit Amsterdam and Erasmus University received funding from TKI Dinalog [Grant 2023-1-307TKI]. Some of this work has been executed under the TKI Dinalog [Grant 2023-1-307TKI]. Part of this work was completed during a research visit made possible by a [Distinguished Visitor Award] from the University of Auckland. Supplemental Material: The online appendix and data files are available at https://doi.org/10.1287/mnsc.2022.04024 .
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- Award ID(s):
- 2035086
- PAR ID:
- 10522660
- Publisher / Repository:
- INFORMS
- Date Published:
- Journal Name:
- Management Science
- Volume:
- To appear.
- ISSN:
- 0025-1909
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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