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

8 years 17 days ago

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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: (i) wireless coverage of targeted geographical regions with guaranteed signal quality and minimum transmission power, (ii) computing real-time certiﬁcates of collision avoidance for a simple model of an unmanned vehicle (UV) navigating through a cluttered environment, and (iii) 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 ap...

Amir Ali Ahmadi, Anirudha Majumdar

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