References
- Lotov A , Bushenkov VA , Kamenev GK . Interactive decision maps: approximation and visualization of pareto frontier. Springer Science & Business Media: New York; 2004.
- McClure DE , Vitale RA . Polygonal approximation of plane convex bodies. J Math Anal Appl. 1975;51(2):326–358.
- Kamenev GK . A class of adaptive algorithms for approximating convex bodies by polyhedra. Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki. Comput Math Math Phys. 1992;32(1):136–152.
- Kamenev GK . Duality theory of optimal adaptive methods for polyhedral approximation of convex bodies. Comput Math Math Phys. 2008;48(3):376–394.
- Lotov AV , Pospelov AI . The modified method of refined bounds for polyhedral approximation of convex polytopes. Comput Math Math Phys. 2008;48(6):933–941.
- Kamenev GK , Pospelov AI . Polyhedral approximation of convex compact bodies by filling methods. Comput Math Math Phys. 2012;52(5):680–690.
- Dudov S , Osiptsev M . Uniform estimation of a convex body by a fixed-radius ball. J Optim Theory Appl. 2016;171(2):465–480.
- Dey SS , Iroume A , Molinaro M . Some lower bounds on sparse outer approximations of polytopes. Oper Res Lett. 2015;43(3):323–328.
- Löhne A , Weißing B . Equivalence between polyhedral projection, multiple objective linear programming and vector linear programming. Math Methods Oper Res. 2016;84(2):411–426.
- Benson H . An outer approximation algorithm for generating all efficient extreme points in the outcome set of a multiple objective linear programming problem. J Global Optim. 1998;13:1–24.
- Ehrgott M , Shao L , Schöbel A . An approximation algorithm for convex multi-objective programming problems. J Global Optim. 2011;50(3):397–416.
- Löhne A , Rudloff B , Ulus F . Primal and dual approximation algorithms for convex vector optimization problems. J Global Optim. 2014;60(4):713–736.
- Miettinen K . Nonlinear multiobjective optimization. Springer Science & Business Media: Boston; 1999.
- Löhne A , Weißing B . Bensolve - vlp solver, version 2.0.1, 2000. Available from: http://www.bensolve.org
- Varaiya P . Reach set computation using optimal control. In: Inan MK , Kurshan RP , editor. Verification of digital and hybrid systems. Springer: Heidelberg; 2000. p. 323–331.
- Baier R , Büskens C , Chahma IA . Approximation of reachable sets by direct solution methods for optimal control problems. Optim Methods Softw. 2007;22:433–452.
- Kurzhanski AB , Varaiya P . Ellipsoidal techniques for reachability analysis: internal approximation. Syst Control Lett. 2000;41:201–211.
- Kurzhanski AB , Varaiya P . On ellipsoidal techniques for reachability analysis. part I: external approximations. Optim Methods Softw. 2002;17:177–206.
- Filippova T . Differential equations for ellipsoidal estimates for reachable sets of a nonlinear dynamical control system. Proc Steklov Inst Math. 2010;271:75–84.
- Girard A , Le Guernic C , Maler O . Efficient computation of reachable sets of linear time-invariant systems with inputs. In: Hespanha J , Tiwari A , editor. Hybrid systems: computation and control. Vol. 3927. Springer: Berlin Heidelberg; 2006. p. 257–271.
- Dontchev A , Farkhi E . Error estimates for discretized differential inclusions. Computing. 1989;41:349–358.
- Baier R , Gerdts M , Xausa I . Approximation of reachable sets using optimal control algorithms. Numer Algebra Control Optim. 2013;3:519–548.