NDLI: Multicriteria optimization of convex dynamical systems

Content Provider	Springer Nature Link
Author	Lotov, A. V.
Copyright Year	2009
Abstract	We suggest an approach to the solution of multicriteria optimization problems for dynamical systems described by differential inclusions. The investigation is restricted to dynamical systems with concave differential inclusion, for which the trajectory tube is convex. Such systems are typical of economic models. We assume that the criteria for the choice of the solution depend on the system state at a given terminal time and are related to it by sufficiently arbitrary functions. The approach is based on the interactive visualization of the Pareto frontier, which is carried out by approximating the reachable set of the dynamical system and the Edgeworth-Pareto set of feasible criteria vectors.To approximate the reachable set at the terminal time, we use the method of polyhedral approximation of multidimensional convex compact sets (the method of refinement of estimates), which is characterized by an asymptotically optimal order of the number of vertices of the approximating polyhedron and the number of measurements of the support function and by the optimal order of the convergence rate. The suggested approach is used for the case in which the dimension of the state space of the dynamical system does not exceed 6 and the number of criteria does not exceed 8.
Starting Page	1669
Ending Page	1680
Page Count	12
File Format	PDF
ISSN	00122661
Journal	Differential Equations
Volume Number	45
Issue Number	11
e-ISSN	16083083
Language	English
Publisher	SP MAIK Nauka/Interperiodica
Publisher Date	2009-12-23
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Difference and Functional Equations Partial Differential Equations Ordinary Differential Equations
Content Type	Text
Resource Type	Article
Subject	Analysis

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