A variational problem and optimal control

Hang-Chin Lai; Jin-Chirng Lee; Shuh-Jye Chern

doi:10.3934/jimo.2011.7.967

Article Contents

2011, Volume 7, Issue 4: 967-975. Doi: 10.3934/jimo.2011.7.967

This issue Previous Article A new dynamic geometric approach for empirical analysis of financial ratios and bankruptcy Next Article A smoothing homotopy method based on Robinson's normal equation for mixed complementarity problems

A variational problem and optimal control

1.
Chung Yuan Christian University, Chung Li
2.
National Tsing Hua University, Hsinchu

Received: January 2011

Revised: June 2011

Published: October 2011

Abstract / Introduction Related Papers Cited by

Abstract

A variational problem involving two variables, the state and the control variables, is reduced to another variational problem in which the objective has no control variable, but the constrained identity has one. We then establish that the two problems are equivalent with the same optimal (state) solution under some conditions.

Keywords:

Mathematics Subject Classification: Primary: 46G12, 28B20; Secondary: 54C65.

Citation:

Related Papers

Cited by

References

[1]	G. P. Akilov and L. V. Kantorovich, "Functional Analysis," 2^nd edition, Translated from the Russian by Howard L. Silcock, Pergamon Press, Oxford-Elmsford, NY, 1982.
[2]	H. C. Lai, Duality of Banach function spaces and Radon Nikodym property, Acta Mathematics Hungarica, 47 (1986), 45-52.doi: 10.1007/BF01949123.
[3]	H. C. Lai and J. W. Chen, On the generalized Euler-Lagrange equations, Journal of Mathematical Analysis and Applications, 213 (1997), 681-697.
[4]	H. C. Lai and J. C. Lee, Convergent Theorems and $L$^$p$-selections for Banach-valued multifunctions, Nihonkai Math. Journal, 4 (1993), 163-180.
[5]	H. C. Lai and J. C. Lee, Integration Theory for Banach-valued multifunctions, Indian Journal of Mathematics, 34 (1992), 265-284.
[6]	H. C. Lai and J. C. Lee, Integral representations and convergences for Banach-valued multifunctions, Fixed Point Theory and Applications (Halifax, NS, 1991), World Scientific Publ., River Edge, NJ, (1992), 169-188.
[7]	H. C. Lai and L. J. Lin, The Fenchel-Moreau theorem for set functions, Proceedings of the American Mathematics Society, 103 (1988), 85-90.doi: 10.1090/S0002-9939-1988-0938649-4.
[8]	C. Olech, Existence theorem in optimal control problems involving multiple integrals, Journal of Differential Equations, 6 (1969), 512-526.doi: 10.1016/0022-0396(69)90007-2.
[9]	J. P. Raymond, Existence theorems in optimal control problems without convexity assumptions, Journal of Optimization Theory and Applications, 67 (1990), 109-132.doi: 10.1007/BF00939738.
[10]	R. T. Rockafellar, Existence theorems for general control problems of Bolza and Lagrange, Advances in Mathematics, 15 (1975), 312-333.doi: 10.1016/0001-8708(75)90140-1.