Approximation of convex bodies by multiple objective optimization and an application in reachable sets

Abstract

In this paper, we focus on approximating convex compact bodies. For a convex body described as the feasible set in objective space of a multiple objective programme, we show that finding it is equivalent to finding the non-dominated set of a multiple objective programme. This equivalence implies that convex bodies can be approximated using multiple objective optimization algorithms. Therefore, we propose a revised outer approximation algorithm for convex multiple objective programming problems to approximate convex bodies. Finally, we apply the algorithm to solve reachable sets of control systems and use numerical examples to show the effectiveness of the algorithm.

Keywords:

• Convex body
• multiple objective programme
• inner approximation
• outer approximation
• reachable set

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was partially supported by Beijing Natural Science Foundation [grant number 4152034] and National Natural Science Foundation of China [grant number 11471217].