Details
| Original language | English |
|---|---|
| Pages (from-to) | 619-634 |
| Number of pages | 16 |
| Journal | Journal of Optimization Theory and Applications |
| Volume | 94 |
| Issue number | 3 |
| Publication status | Published - Sept 1997 |
Abstract
An optimal control problem with four linear controls describing a sophisticated concern model is investigated. The numerical solution of this problem by combination of a direct collocation and an indirect multiple shooting method is presented and discussed. The approximation provided by the direct method is used to estimate the switching structure caused by the four controls occurring linearly. The optimal controls have bang-bang subarcs as well as constrained and singular subarcs. The derivation of necessary conditions from optimal control theory is aimed at the subsequent application of an indirect multiple shooting method but is also interesting from a mathematical point of view. Due to the linear occurrence of the controls, the minimum principle leads to a linear programming problem. Therefore, the Karush-Kuhn-Tucker conditions can be used for an optimality check of the solution obtained by the indirect method.
Keywords
- direct collocation method, indirect multiple shooting method, linear controls, Microeconomic models, minimum principle as LP, necessary conditions, optimal control, singular subarcs
ASJC Scopus subject areas
- Mathematics(all)
- Control and Optimization
- Decision Sciences(all)
- Management Science and Operations Research
- Mathematics(all)
- Applied Mathematics
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In: Journal of Optimization Theory and Applications, Vol. 94, No. 3, 09.1997, p. 619-634.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - In optimal control problem in economics with four linear controls
AU - Koslik, B.
AU - Breitner, M. H.
N1 - Copyright: Copyright 2012 Elsevier B.V., All rights reserved.
PY - 1997/9
Y1 - 1997/9
N2 - An optimal control problem with four linear controls describing a sophisticated concern model is investigated. The numerical solution of this problem by combination of a direct collocation and an indirect multiple shooting method is presented and discussed. The approximation provided by the direct method is used to estimate the switching structure caused by the four controls occurring linearly. The optimal controls have bang-bang subarcs as well as constrained and singular subarcs. The derivation of necessary conditions from optimal control theory is aimed at the subsequent application of an indirect multiple shooting method but is also interesting from a mathematical point of view. Due to the linear occurrence of the controls, the minimum principle leads to a linear programming problem. Therefore, the Karush-Kuhn-Tucker conditions can be used for an optimality check of the solution obtained by the indirect method.
AB - An optimal control problem with four linear controls describing a sophisticated concern model is investigated. The numerical solution of this problem by combination of a direct collocation and an indirect multiple shooting method is presented and discussed. The approximation provided by the direct method is used to estimate the switching structure caused by the four controls occurring linearly. The optimal controls have bang-bang subarcs as well as constrained and singular subarcs. The derivation of necessary conditions from optimal control theory is aimed at the subsequent application of an indirect multiple shooting method but is also interesting from a mathematical point of view. Due to the linear occurrence of the controls, the minimum principle leads to a linear programming problem. Therefore, the Karush-Kuhn-Tucker conditions can be used for an optimality check of the solution obtained by the indirect method.
KW - direct collocation method
KW - indirect multiple shooting method
KW - linear controls
KW - Microeconomic models
KW - minimum principle as LP
KW - necessary conditions
KW - optimal control
KW - singular subarcs
UR - http://www.scopus.com/inward/record.url?scp=0031513402&partnerID=8YFLogxK
U2 - 10.1023/A:1022648900252
DO - 10.1023/A:1022648900252
M3 - Article
AN - SCOPUS:0031513402
VL - 94
SP - 619
EP - 634
JO - Journal of Optimization Theory and Applications
JF - Journal of Optimization Theory and Applications
SN - 0022-3239
IS - 3
ER -