Some applications of polynomial optimization in operations research and real-time decision making
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Author(s)
Ahmadi, Amir Ali
Majumdar, Anirudha
Date Issued
June 2015
Journal
Optimization Letters
Publisher
Springer Berlin Heidelberg
Citation
Ahmadi, Amir Ali, and Anirudha Majumdar. “Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making.” Optim Lett 10, no. 4 (June 11, 2015): 709–729.
Version
Author's final manuscript
Abstract
We 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.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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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.
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DOI of Published Version
https://doi.org/10.1007/s11590-015-0894-3
