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 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
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spelling	my-uthm-ep.3312021-07-22T07:01:59Z A nonstandard optimal control problem arising in an economics application: for royalty payment with piecewise function 2018-11 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 http://eprints.uthm.edu.my/331/ http://eprints.uthm.edu.my/331/1/24p%20WAN%20NOOR%20AFIFAH%20WAN%20AHMAD.pdf text en public http://eprints.uthm.edu.my/331/2/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20COPYRIGHT%20DECLARATION.pdf text en staffonly http://eprints.uthm.edu.my/331/3/WAN%20NOOR%20AFIFAH%20WAN%20AHMAD%20WATERMARK.pdf text en validuser mphil masters Universiti Tun Hussein Onn Malaysia Faculty of Applied Sciences and Technology
institution	Universiti Tun Hussein Onn Malaysia
collection	UTHM Institutional Repository
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
qualification_name	Master of Philosophy (M.Phil.)
qualification_level	Master's degree
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
granting_institution	Universiti Tun Hussein Onn Malaysia
granting_department	Faculty of Applied Sciences and Technology
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
_version_	1747830584277729280

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

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