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A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function

A current Optimal Control (OC) problem in the region of financial aspects has numerical properties that do not fall into the standard OC problem formulation. In this study, the state value at the final time is y T   z where it is free and a priori unknown. Furthermore, the Lagrangian integrand in...

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Main Author: Wan Ahmad, Wan Noor Afifah
Format: Thesis
Language:English
English
English
Published: 2018
Subjects:
QA273-280 Probabilities. Mathematical statistics
Online Access:http://eprints.uthm.edu.my/331/1/24p%20WAN%20NOOR%20AFIFAH%20WAN%20AHMAD.pdf
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http://eprints.uthm.edu.my/331/3/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20WATERMARK.pdf
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spelling my.uthm.eprints.3312021-07-22T07:01:59Z http://eprints.uthm.edu.my/331/ A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function Wan Ahmad, Wan Noor Afifah QA273-280 Probabilities. Mathematical statistics A current Optimal Control (OC) problem in the region of financial aspects has numerical properties that do not fall into the standard OC problem formulation. In this study, the state value at the final time is y T   z where it is free and a priori unknown. Furthermore, the Lagrangian integrand in the functional is a piecewise constant system of the unknown value y T . This is not categorized, as in a standard OC problem, and cannot be settled by utilizing Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard case, a free final state value y T  yields a necessary boundary condition pT   0 where pt  is the costate variable. Since the integrand is an element of y T , the new necessary condition is that y T  ought to be equivalent to a certain integral that is a continuous system of y T   z. This study presents a continuous approximation of the piecewise constant integrand function by utilizing a hyperbolic tangent (tanh) approach, and solves a case utilizing a C++ shooting algorithm with a Newton iteration to take care of the Two-Point Boundary Value Problem (TPBVP). The minimizing free value y T  is computed in an outer loop iteration utilizing the Golden Section Search algorithm. At the end of the study, a comparative discrete-time nonlinear programming (NLP) results are also presented. 2018-11 Thesis NonPeerReviewed text en http://eprints.uthm.edu.my/331/1/24p%20WAN%20NOOR%20AFIFAH%20WAN%20AHMAD.pdf text en http://eprints.uthm.edu.my/331/2/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20COPYRIGHT%20DECLARATION.pdf text en http://eprints.uthm.edu.my/331/3/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20WATERMARK.pdf Wan Ahmad, Wan Noor Afifah (2018) A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function. Masters thesis, Universiti Tun Hussein Onn Malaysia.
institution Universiti Tun Hussein Onn Malaysia
building UTHM Library
collection Institutional Repository
continent Asia
country Malaysia
content_provider Universiti Tun Hussein Onn Malaysia
content_source UTHM Institutional Repository
url_provider http://eprints.uthm.edu.my/
language English
English
English
topic QA273-280 Probabilities. Mathematical statistics
spellingShingle QA273-280 Probabilities. Mathematical statistics
Wan Ahmad, Wan Noor Afifah
A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
description A current Optimal Control (OC) problem in the region of financial aspects has numerical properties that do not fall into the standard OC problem formulation. In this study, the state value at the final time is y T   z where it is free and a priori unknown. Furthermore, the Lagrangian integrand in the functional is a piecewise constant system of the unknown value y T . This is not categorized, as in a standard OC problem, and cannot be settled by utilizing Pontryagin's Minimum Principle with the standard boundary conditions at the final time. In the standard case, a free final state value y T  yields a necessary boundary condition pT   0 where pt  is the costate variable. Since the integrand is an element of y T , the new necessary condition is that y T  ought to be equivalent to a certain integral that is a continuous system of y T   z. This study presents a continuous approximation of the piecewise constant integrand function by utilizing a hyperbolic tangent (tanh) approach, and solves a case utilizing a C++ shooting algorithm with a Newton iteration to take care of the Two-Point Boundary Value Problem (TPBVP). The minimizing free value y T  is computed in an outer loop iteration utilizing the Golden Section Search algorithm. At the end of the study, a comparative discrete-time nonlinear programming (NLP) results are also presented.
format Thesis
author Wan Ahmad, Wan Noor Afifah
author_facet Wan Ahmad, Wan Noor Afifah
author_sort Wan Ahmad, Wan Noor Afifah
title A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
title_short A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
title_full A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
title_fullStr A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
title_full_unstemmed A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
title_sort nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function
publishDate 2018
url http://eprints.uthm.edu.my/331/1/24p%20WAN%20NOOR%20AFIFAH%20WAN%20AHMAD.pdf
http://eprints.uthm.edu.my/331/2/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20COPYRIGHT%20DECLARATION.pdf
http://eprints.uthm.edu.my/331/3/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20WATERMARK.pdf
http://eprints.uthm.edu.my/331/
_version_ 1738580723276709888
score 13.211869

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