Some Applications of Polynomial Optimization in Operations Research and Real-Time Decision Making
Amir Ali Ahmadi(a_a_aprinceton.edu)
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: (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 applications of sum of squares techniques in optimization and control. No knowledge in dynamics and control is assumed from the reader.
Keywords: polynomial optimization, semidefinite programming, second order cone programming, algebraic techniques in optimization, real-time optimization
Category 1: Convex and Nonsmooth Optimization (Convex Optimization )
Category 2: Linear, Cone and Semidefinite Programming
Category 3: Global Optimization
Citation: To appear in Optimization Letters.
Entry Submitted: 04/22/2015
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