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The general theory has naturally developed out of the study of special problems. It is therefore useful to get a first impression by looking at the ‘classic’ problems. We will have a first look at some elementary examples to get an idea of the kind of problems which will be stated more precisely and treated in more depth later on. Consequently, we will often not go into too much detail in this introductory chapter.
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References
W. Karush (1939): Minima of Functions of Several Variables with Inequalities as Side Conditions. Univ. of Chicago Master’s Thesis
F. John (1948): Extremum Problems with Inequalities as Subsidiary Conditions. In: Studies and Essays. Courant Anniversary Volume. Interscience, New York, pp. 187–204
C. F. Gauss (1831): Brief an Schumacher. Werke Bd. 8, p. 138
A. Cauchy (1847): Méthode générale pour la résolution des sys- tèmes d’équations simultanées. Comptes Rendus Acad. Sci. Paris 25, pp. 536–538
K. Levenberg (1944): A Method for the Solution of Certain Non-linear Problems in Least Squares. Quart. Appl. Math. 2, 164–168
D. W. Marquardt (1963): An Algorithm for Least-Squares Estimation of Nonlinear Parameters. SIAM J. Appl. Math. 11, pp. 431–441
S.Ṁ. Goldfeld, R.Ė. Quandt, H.Ḟ. Trotter (1966): Maximization by Quadratic Hill-Climbing. Econometrica 34, pp. 541–551
R. V. Southwell (1940): Relaxation Methods in Engineering Science. Clarendon Press, Oxford
W. C. Davidon (1991): Variable Metric Method for Minimization. SIAM J. Optimization 1, pp. 1–17
A. Fiacco, G. McCormick (1990): Nonlinear Programming — Sequential Unconstrained Minimization Techniques. SIAM, Philadelphia
E. Hairer (2001): Introduction à l’Analyse Numérique. Lecture Notes, Genève, p. 158
M. C. Bartholomew-Biggs (2005): Nonlinear Optimization with Financial Applications. Kluwer, Boston, Dordrecht, London
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Forst, W., Hoffmann, D. (2010). Introduction. In: Optimization—Theory and Practice. Springer Undergraduate Texts in Mathematics and Technology . Springer, New York, NY. https://doi.org/10.1007/978-0-387-78977-4_1
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DOI: https://doi.org/10.1007/978-0-387-78977-4_1
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