To refer to this page use:
|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.|
|Citation:||Ahmadi, 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/s11590-015-0894-3|
|Pages:||709 - 729|
|Type of Material:||Journal Article|
|Journal/Proceeding Title:||Optimization Letters|
Items in OAR@Princeton are protected by copyright, with all rights reserved, unless otherwise indicated.