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Record link: 
http://hdl.handle.net/20.500.12708/144831
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Title: 
Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics
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Citation: 
Lykina, V., & Pickenhain, S. (2018). Pontryagin Type Maximum Principle for budget-constrained infinite horizon optimal control problems with linear dynamics. Journal of Mathematical Analysis and Applications, 457(2), 1591–1612. https://doi.org/10.1016/j.jmaa.2017.08.002
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Publisher DOI: 
10.1016/j.jmaa.2017.08.002
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Publication Type: 
Article - Original Research Article
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Authors: 
Lykina, Valeriya 
Pickenhain, Sabine 
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Organisational Unit: 
E105-04 - Forschungsbereich Variationsrechnung, Dynamische Systeme und Operations Research 
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Journal: 
Journal of Mathematical Analysis and Applications 
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ISSN: 
0022-247X
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Date (published): 
2018
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Number of Pages: 
22
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Peer reviewed: 
Yes
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Keywords: 
Applied Mathematics; Analysis; Optimal control; Budget constraint; Infinite horizon; Pontryagin Type Maximum Principle; Weighted Sobolev spaces; Linear-quadratic regulator
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Abstract: 
In this paper a class of infinite horizon optimal control problems with an isoperimetrical constraint, also interpreted as a budget constraint, is considered. Herein a linear both in the state and in the control dynamic is allowed. The problem setting includes a weighted Sobolev space as the state space. For this class of problems, we establish the necessary optimality conditions in form of a Pontryagin Type Maximum Principle including a transversality condition. The proved theoretical result is applied to a linear-quadratic regulator problem.
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Research Areas: 
Mathematical Methods in Economics: 60%
Fundamental Mathematics Research: 20%
Modelling and Simulation: 20%
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Science Branch: 
Mathematik
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