Abstract
We transform a 2-dimensional second-order cone program to a standard linear program in order to pivot a vector based on its three states. Related properties of the transformation are given. Based on the transformation, we interpret the simplex method and its sensitivity analysis for the 2-dimensional second-order cone programming, especially the state changes. Finally, we give some applications of the 2-dimensional second-order cone programming.
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Alizadeh, F., Goldfarb, D.: Second-order cone programming. Math. Program 95(1, Ser. B), 3–51 (2003)
Lobo, M.S., Vandenberghe, L., Boyd, S., Lebret, H.: Applications of second-order cone programming. Linear Algebra Appl. 284(1-3), 193–228 (1998)
Vanderbei, R.J.: Linear programming: foundations and extensions. Kluwer Academic Publishers, Boston (1996)
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© 2006 Springer-Verlag Berlin Heidelberg
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Xia, Y. (2006). A Note on the Simplex Method for 2-Dimensional Second-Order Cone Programming. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds) Computational Science – ICCS 2006. ICCS 2006. Lecture Notes in Computer Science, vol 3991. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11758501_21
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DOI: https://doi.org/10.1007/11758501_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-34379-0
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