Keywords
- Minimal Surface
- Quadratic Programming
- Quadratic Programming Problem
- Soap Film
- Weber Problem
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References
Collatz, L. and W. Wetterling: Optimierungsaufgaben. 2nd ed. Heidelberger Taschenbücher, Vol. 15. Berlin, Heidelberg, New York: Springer-Verlag 1971.
Concus, P.: Numerical solution of the minimal surface equation. Math. Comput. 21, 340–350 (1967).
Courant, R.: Dirichlet's Principle, Conformal Mapping, and Minimal Surfaces. Pure and Applied Mathematics, Vol. III. New York, London: Interscience Publishers 1950.
Eaves, B. C.: On quadratic programming. Management Sci. 17, 698–711 (1970/71).
Eckhardt, U.: Quadratic programming by successive overrelaxation. KFA Jülich Research Report, Jül-1064-MA, April 1974.
Hinata, M., M. Shimasaki and T. Kiyono: Numerical solution of Plateau's problem by a finite element method. Math. Comput. 28, 45–60 (1974).
Katz, I. N.: On the convergence of a numerical scheme for solving some locational equilibrium problems. SIAM J. Appl. Math. 17, 1224–1231 (1969).
Kuhn, H. W.: A note on Fermat's problem. Math. Programming 4, 98–107 (1973).
Lemke, C. E.: On complementary pivot theory. In: G. B. Dantzig and A. F. Veinott, eds.: Mathematics of the Decision Sciences, Part I. Lectures in Applied Mathematics, Vol. 11, pp. 95–114. Providence: American Mathematical Society 1968.
Mangasarian, O. L.: Nonlinear Programming. New York etc.: McGraw-Hill Book Company 1969.
Meis, Th.: Zur Diskretisierung nichtlinearer elliptischer Differentialgleichungen. Computing 7, 344–352 (1971).
Meis, Th. and W. Törnig: Diskretisierungen des Dirichletproblems nichtlinearer elliptischer Differentialgleichungen. In: B. Brosowski and E. Martensen, eds.: Methoden und Verfahren der mathematischen Physik, Band 8, pp. 47–72. Mannheim/Wien/Zürich: Bibliographisches Institut, B.I.-Wissenschaftsverlag 1973.
Mittelmann, H. D.: Die Approximation der Lösungen gemischter Randwertprobleme quasilinearer elliptischer Differentialgleichungen. Technische Hochschule Darmstadt, Fachbereich Mathematik, Preprint Nr. 114, Januar 1974.
Nitsche, J. C. C.: Variational problems with inequalities as boundary conditions, or, How to fashion a cheap hat for Giacometti's brother. Arch. Rat. Mech. Anal. 35, 83–113 (1969).
Nitsche, J. C. C.: Minimal surfaces with partially free boundary. Annales Academiae Scientiarum Fennicae Ser. A. I. Mathematica. No. 483 (1971).
Thomas, J.: Zur Statik eines gewissen Federsystems in En. Math. Nachr. 23, 185–195 (1961).
Weiszfeld, E.: Sur le point par lequel la somme des distances de n points donnés est minimum. Tôhoku Mathematics J. 43, 355–386 (1937).
Wilson, W. L., Jr.: On discrete Dirichlet and Plateau problems. Numer. Math. 3, 359–373 (1961).
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Eckhardt, U. (1975). On an optimization problem related to minimal surfaces with obstacles. In: Bulirsch, R., Oettli, W., Stoer, J. (eds) Optimization and Optimal Control. Lecture Notes in Mathematics, vol 477. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0079169
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DOI: https://doi.org/10.1007/BFb0079169
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