Abstract
The calculus of variations treats the problem of finding extrema of functionals, i.e. real valued functions having functions as “independent variables”. Below, necessary conditions (the Euler-Lagrange equation (15.1), the solutions of which are called extremals) are stated for some different kinds of variational problems. Sufficient conditions can be formulated (e.g. Weierstrass’ theory on strong extrema). However, “common sense” may often be used to establish the sufficiency.
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© 2004 Springer-Verlag Berlin Heidelberg
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Råde, L., Westergren, B. (2004). Optimization. In: Mathematics Handbook for Science and Engineering . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-08549-3_15
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DOI: https://doi.org/10.1007/978-3-662-08549-3_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05936-0
Online ISBN: 978-3-662-08549-3
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