The Lagrange multiplier method in the finite convex programming problem |
Zhiltsov A. V., Namm R. V. |
2015, issue 1, P. 53-60 |
Abstract |
In this paper we investigate the possibility of using the modified Lagrange’s function for solving of a finite-dimensional convex programming problem. Convergence of the modified duality method is proved under the most general assumptions concerning of initial problem. |
Keywords: Lagrange multiplier method, convex optimization, finite convex programming |
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References |
[1] D. Bertsekas, Uslovnaja optimizacija i metody mnozhitelej Lagranzha, Radio isvjaz', M, 1987. [2] B.T. Poljak, Vvedenie v optimizaciju, Nauka, M, 1983. [3] E. G. Gol'shtejn, N. V. Tret'jakov, Modificirovannye funkcii Lagranzha. Teorija i metody optimizacii, Nauka, M, 1989. [4] D.P. Bertsekas, Convex Optimization Theory, Athena Scientific, Belmont, Masachusetts, 2009. [5] K. Grossman, A. A. Kaplan, Nelinejnoe programmirovanie na osnove bezuslovnoj minimizacii, Nauka, Novosibirsk, 1981. [6] A. S. Antipin, A. I. Golikov, E. V. Horoshilova, “Funkcija chuvstvitel'nosti, ee svojstva i prilozhenija”, Zh. vychisl. matem. i matem. fiz, 51:12 (2011), 1–17. [7] I. Jekland, R. Temam, Vypuklyj analiz i variacionnye problemy, M, Mir, 1979. [8] A. Kufner, S. Fuchik, Nelinejnye differencial'nye uravnenija, M, Nauka, 1988. [9] Ju.E. Nesterov, Vvedenie v vypukluju optimizaciju, M, MCNMO, 2010. |