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An Observation on Two Methods of Obtaining Solutions to Variational Problems

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Abstract

In this paper, we compare two methods for obtaining solutions for free problems in the calculus of variations. The first is due to Carathéodory (Ref. 1) and the second due to Leitmann (Ref. 2). Both methods introduce the notion of equivalent variational problems. Using either approach, an auxiliary problem is obtained for which the solution is more easily obtained. We compare both approaches by using each to solve the same class of examples. We conclude our discussion by unifying the two approaches into one and illustrating the potential of this new method through the use of an elementary example.

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References

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Authors and Affiliations

  1. Department of Mathematics, University of Toledo, Toledo, Ohio

    D.A. Carlson (Professor)

Authors
  1. D.A. Carlson
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Carlson, D. An Observation on Two Methods of Obtaining Solutions to Variational Problems. Journal of Optimization Theory and Applications 114, 345–361 (2002). https://doi.org/10.1023/A:1016035718160

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  • DOI: https://doi.org/10.1023/A:1016035718160

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