Abstract
An optimization problem consists in minimizing a function f : M → IR on a given set M. \( {\bar x} \) ∈ M is a solution of
, if \( {\bar x} \) ≤ f(x) for all x ∈ M. f is often called cost or objective function, M the set of feasible solutions.
Bei dem studio der Mathematik kann wohl nichts stärkeren Trost bei Unverständlichkeiten gewähren, als daß es sehr viel schwerer ist eines anderen Meditata zu verstehen, als selbst zu meditieren. G. Chr. Lichtenberg
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Literature
1: One finds a survey of optimization problems in elementary geometry in ZACHARIAS [80], STURM [12]. Historical remarks on the FERMAT problem are to be found in KUHN [47]. A good survey of the significance of the FERMAT-WEBER problem in location theory is BLOECH [7].
2: For a very good short introduction to the history and objectives of the calculus of variations we refer the reader to the introduction of BLANCHARD-BRUENING [5], for a more ex tensive presentation to GOLDSTINE [29], A relatively elemen¬tary and very readable book about the calculus of variations with many historical remarks (in particular about the brachy- stochrone problem) and examples is SMITH [69].
3.2 GOLDSTINE [28] makes historical remarks about the work of GAUSS and LEGENDRE on the method of least squares. Further literature about investigations on the choice of starting approximation for the computation of square roots can be found in an essay by MEINARDUS-TAYLOR [60].
4.: We refer to DANTZIG [20] for interesting remarks on the history of linear programming.
5: For further examples of optimal control problems see e. g. BRYSON-HO [11] and KNOWLES [43].
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© 1984 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Werner, J. (1984). Introduction, Examples, Survey. In: Optimization Theory and Applications. Advanced Lectures in Mathematics. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-84035-6_1
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DOI: https://doi.org/10.1007/978-3-322-84035-6_1
Publisher Name: Vieweg+Teubner Verlag, Wiesbaden
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