On the Leitmann Equivalent Problem Approach

The purpose of this paper is to show how Leitmann’s equivalent problem approach ties in with the classical notions of the calculus of variations and how it can be exploited to give a rapid and elegant approach to the Weierstrass theory of sufficient conditions. Fixed, free and constrained endpoint conditions are considered.

[1]  George Leitmann,et al.  A note on absolute extrema of certain integrals , 1967 .

[2]  G. Leitmann,et al.  On a Class of Direct Optimization Problems , 2001 .

[3]  D. A. Carlson.  An Observation on Two Methods of Obtaining Solutions to Variational Problems , 2002 .

[4]  George Leitmann.  On a class of direct optimization problems 1,2 , 2002 .

[5]  A. Kneser,et al.  Lehrbuch der Variationsrechnung , 1925 .

[6]  George Leitmann,et al.  Fields of extremals and sufficient conditions for the simplest problem of the calculus of variations , 2008, J. Glob. Optim..

[7]  Leonhard Euler.  Methodus inveniendi lineas curvas maximi minimive proprietate gaudentes, sive solutio problematis isoperimetrici latissimo sensu accepti , 2013, 1307.7187.

[8]  F. O. O. Wagener,et al.  On conjugate points and the Leitmann equivalent problem approach , 2010, Appl. Math. Comput..

[9]  M. Giaquinta,et al.  Calculus of Variations I , 1995 .

[10]  C. Carathéodory,et al.  Variationsrechnung und partielle Differentialgleichungen erster Ordnung , 1935 .

[11]  Fields of Extremals and Sufficient Conditions for the Simplest Problem of the Calculus of Variations in n-Variables , 2009 .

[12]  Hamel.  Constantin Caratheodory, Prof. an der Universität München, Variationsrechnung und partielle Differentialgleichungen erster Ordnung. XI + 407 S. m. 31 Fig. im Text. Leipzig und Berlin 1935, B. G. Teubner Verlag. Preis 22 M , 1935 .

[13]  V. Arnold.  Mathematical Methods of Classical Mechanics , 1974 .