Hyperplane Arrangements in Mixed-Integer Programming Techniques. Collision avoidance application with Zonotopic Sets

Citation:

F. Stoican, Prodan, I., and Olaru, S., “Hyperplane Arrangements in Mixed-Integer Programming Techniques. Collision avoidance application with Zonotopic Sets”, in Proceedings of the 2013 European Control Conference, Zurich, Switzerland, 2013, p. 3155-3160.

Date Published:

17-19 July

Accession Number:

13950603

Abstract:

The current paper addresses the problem of minimizing the computational complexity of optimization problems with non-convex and possibly non-connected feasible region of polyhedral type. Using hyperplane arrangements and Mixed-Integer Programming we provide an efficient description of the feasible region in the solution space. Moreover, we exploit the geometric properties of the hyperplane arrangements and adapt this description in order to provide an efficient solution of the mixed-integer optimization problem. Furthermore, a zonotopic representation of the sets appearing in the problem is considered. The advantages of this representation are highlighted and exploited through proof of concepts illustrations as well as simulation results.