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Necessary optimality conditions for bicriterion discrete optimal control problems

Published online by Cambridge University Press:  17 February 2009

X. Q. Yang  and
K. L. Teo
X. Q. Yang
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands, 6907, W.A., Australia
K. L. Teo
Affiliation:
School of Mathematics, Curtin University of Technology, GPO Box U1987, Perth 6845, Australia
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Abstract

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In management science and system engineering, problems with two incommensurate objectives are often detected. Bicriterion optimization finds an optimal solution for the problems. In this paper it is shown that bicriterion discrete optimal control problems can be solved by using a parametric optimization technique with relaxed convexity assumptions. Some necessary optimality conditions for discrete optimal control problems subject to a linear state difference equation are derived. It is shown that in this case no adjoint equation is required.

Type
Research Article
Information
The ANZIAM Journal , Volume 40 , Issue 3 , January 1999 , pp. 392 - 402
Copyright
Copyright © Australian Mathematical Society 1999

References

[1]Boltyanskii, V. G., Optimal Control of Discrete Systems (John Wiley & Sons, New York, Toronto, 1978).Google Scholar
[2]Cai, X., Teo, K. L., Yang, X. Q. and Zhou, X. Y., “Portfolio optimization under l ∞, risk measure”, in 35th IEEE Conference on Decision and Control, Kobe, Japan, 1996.Google Scholar
[3]Clarke, F. H., Optimization and Nonsmooth Analysis (John Wiley & Sons, New York, 1983).Google Scholar
[4]Craven, B. D., Mathematical Programming and Control Theory (Chapman and Hall, London, 1978).CrossRefGoogle Scholar
[5]Craven, B. D., Fractional Programming (Heldermann Verlag, Berlin, 1988).Google Scholar
[6]Geoffrion, A. M., “Solving bicriteria mathematical programs”. Operations Research 15 (1967) 39–54.CrossRefGoogle Scholar
[7]Jeyakumar, V. and Yang, X. Q., “Convex composite multi-objective nonsmooth programming”, Mathematical Programming 59 (1993) 325–343.CrossRefGoogle Scholar
[8]Li, D., “On the minimax solution of multiple linear-quadratic problems”, IEEE Transactions on Automatic Control 35 (1990) 1153–1156.CrossRefGoogle Scholar
[9]Loganathan, G. V., “Benefit-cost problems: a bi-criteria approach”, Engineering Optimization 13 (1988) 225–234.CrossRefGoogle Scholar
[10]Luc, D. T., Theory of Vector Optimization, Lecture Notes in Economics and Mathematical Systems (Springer, Berlin, 1989).CrossRefGoogle Scholar
[11]Marchi, A., On the relationships between bicriteria problems and nonlinear programming. Lecture Notes in Economics and Mathematical Systems, 405 (Springer, Berlin, 1994).Google Scholar
[12]Mond, B., “On algorithmic equivalence in linear fractional programming”, Mathematics of Computation 37 (1981) 185–187.CrossRefGoogle Scholar
[13]Pytlak, R. and Malinowski, K., “Optimal scheduling of reservior releases during flood: deterministic optimization problem”, J. Optim. Theory Appl. 61 (1989) 409–431.CrossRefGoogle Scholar
[14]Sandblom, C. L., Eiselt, H. A. and Jornsten, K. O., “Discrete-time optimal control of an economic system using different objective functions”, Optimal Control Applications & Methods 8 (1987) 253–269.CrossRefGoogle Scholar
[15]Teo, K. L., Goh, C. J. and Wong, K. H., A Unified Computational Approach to Optimal Control Problems (Longman Scientific and Technical, New York, 1990).Google Scholar
[16]Yu, P. L., Multiple-Criteria Decision Making (Plenum Press, New York, 1985).CrossRefGoogle Scholar