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Two Direct Methods For Obtaining Solutions To Variational Problems

Author

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  • DEAN A. CARLSON

    (Department of Mathematics, The University of Toledo, W. Bancroft Street, Toledo, Ohio 43606–3390, USA)

Abstract

In this paper we compare two methods for obtaining solutions for free problems in the Calculus of Variations. The first appears at least as early as 1935 and is due to Carathéodory while the second, due to Leitmann, first appears in 1967. 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 this new method's potential through the use of an elementary example.

Suggested Citation

  • Dean A. Carlson, 2004. "Two Direct Methods For Obtaining Solutions To Variational Problems," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 6(01), pages 1-13.
    • Handle: RePEc:wsi:igtrxx:v:06:y:2004:i:01:n:s0219198904000034
    DOI: 10.1142/S0219198904000034
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    Cited by:

    1. Wagener, F.O.O., 2009. "On conjugate points and the Leitmann equivalent problem approach," CeNDEF Working Papers 09-08, Universiteit van Amsterdam, Center for Nonlinear Dynamics in Economics and Finance.

    More about this item

    Keywords

    Direct methods; calculus of variations;

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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