Titlebook: Variational Calculus with Elementary Convexity; John L. Troutman Textbook 19831st edition Springer-Verlag New York Inc. 1983 Convexity.Kon

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Standard Optimization Problemshen “best” can be assessed numerically, then this assessment may be regarded as a real valued function of the method under consideration which is to be optimized — either maximized or minimized. We are interested not only in the optimum values which can be achieved, but also in the method (or methods) which can produce these values.

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Brochure

The Euler-Lagrange EquationsAlthough Jakob Bernoulli’s solution of 1696 to his brother Johann’s problem of the brachistochrone (§1.2) marked the introduction of variational considerations, it was not until the work of Euler (c. 1742) and Lagrange (1755) that the systematic theory now known as the calculus of variations emerged.

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Sufficient Conditions for a MinimumAs we have noted repeatedly, the equations of Euler-Lagrange are necessary but not sufficient to characterize a minimum value for the integral function

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