# Some applications of polynomial optimization in operations research and real-time decision making

## Author(s): Ahmadi, AA; Majumdar, Anirudha

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DC FieldValueLanguage
dc.contributor.authorMajumdar, Anirudha-
dc.date.accessioned2021-10-08T20:20:08Z-
dc.date.available2021-10-08T20:20:08Z-
dc.date.issued2016en_US
dc.identifier.citationAhmadi, AA, Majumdar, A. (2016). Some applications of polynomial optimization in operations research and real-time decision making. Optimization Letters, 10 (709 - 729. doi:10.1007/s11590-015-0894-3en_US
dc.identifier.urihttp://arks.princeton.edu/ark:/88435/pr1qw0t-
dc.description.abstractWe demonstrate applications of algebraic techniques that optimize and certify polynomial inequalities to problems of interest in the operations research and transportation engineering communities. Three problems are considered: (1) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (2) computing real-time certificates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (3) designing a nonlinear hovering controller for a quadrotor UV, which has recently been used for load transportation. On our smaller-scale applications, we apply the sum of squares (SOS) relaxation and solve the underlying problems with semidefinite programming. On the larger-scale or real-time applications, we use our recently introduced “SDSOS Optimization” techniques which result in second order cone programs. To the best of our knowledge, this is the first study of real-time applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader.en_US
dc.format.extent709 - 729en_US
dc.language.isoen_USen_US
dc.relation.ispartofOptimization Lettersen_US
dc.rightsAuthor's manuscripten_US
dc.titleSome applications of polynomial optimization in operations research and real-time decision makingen_US
dc.typeJournal Articleen_US
dc.identifier.doidoi:10.1007/s11590-015-0894-3-
pu.type.symplectichttp://www.symplectic.co.uk/publications/atom-terms/1.0/journal-articleen_US

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