The analysis of the dynamic optimization problem in econophysics from the point of view of the symplectic approach for constrained systems

Cresus F.L. Godinho and Everton M.C. Abreu

Chaos, Solitons & Fractals, 2021, vol. 145, issue C

Abstract: A standard approach to deal with the problems relative to dynamic optimization is the well known Pontryagin method to obtain a concise condition for an optimal control, minimizing the cost functional. In this paper we have proposed a simpler dynamic optimization procedure through a so-called symplectic algorithm. We worked with the analogy between the physical systems at the classical and quantum energy levels. In this way, we started by considering some cost functional f(q,u,t), where q and u are state and control variables, respectively. We have shown that it is possible to investigate the system by means of a symplectic extension, where we can reduce any constrained system into its canonical first order form. Consequently, the dynamics of evolution, usually governed by Dirac’s constraint method, was re-obtained here in a very elegant way. On the other hand, the constraints classification turned out to be different from the one used in Dirac’s procedure. Of course, our analysis is valid for unconstrained systems where the Pontryagin equations are valid too. Four optimization problems were solved.

Keywords: Econophysics; Dynamic optimization problem; Constrained systems (search for similar items in EconPapers)
Date: 2021
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0960077921001053
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:145:y:2021:i:c:s0960077921001053

DOI: 10.1016/j.chaos.2021.110752

Access Statistics for this article

Chaos, Solitons & Fractals is currently edited by Stefano Boccaletti and Stelios Bekiros

More articles in Chaos, Solitons & Fractals from Elsevier
Bibliographic data for series maintained by Thayer, Thomas R. ().