Approximation of convex bodies by multiple objective optimization and an application in reachable sets. (3rd June 2018)

• Record Type: Journal Article
• Authors: Shao, Lizhen; Zhao, Fangyuan; Cong, Yuhao
• Is Part Of: Optimization. Volume 67:Number 6(2018)
• Page Start: 783
• Page End: 796
• Publication Date: 2018-06-03
• Subjects: Convex body -- multiple objective programme -- inner approximation -- outer approximation -- reachable set; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2018.1426583
• Languages: English
• ISSNs: 0233-1934

Abstract

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.