Modified dual scheme for finite-dimensional and infinite-dimensional convex optimization problems |
Vikhtenko E.M., Woo G., Namm R.V. |
2017, issue 2, P. 158-169 |
Abstract |
We consider modified duality methods for the finite dimensional convex optimization problem and the semi-coercive Signorini problem. Duality relations for the direct and dual problems are given without assuming the solvability of dual problem. |
Keywords: variational inequality, convex optimization, Signorini problem, sensitivity functional, Lagrange functional, dual functional. |
Download the article (PDF-file) |
References |
[1] A.M. Khludnev, Zadachi teorii uprugosti v negladkikh oblastiakh, Fizmatlit, M., 2010. [2] E.M. Vikhtenko, R.V. Namm, “O metode dvoistvennosti dlia resheniia model'noi zadachi s treshchinoi”, Tr. in-ta matem. i mekh. UrO RAN, 22:1, (2016), 36–43. [3] K. Grossman, A.A. Kaplan, Nelineinoe programmirovanie na osnove bezuslovnoi optimizatsii, Nauka, Novosibirsk, 1981. [4] I.V. Konnov, Nelineinaia optimizatsiia i variatsionnye neravenstva, Izd-vo Kazanskogo gos. un-ta, Kazan', 2013. [5] E.A. Mukhacheva, G.I. Rubinshtein, Matematicheskoe programmirovanie, Nauka, Novosibirsk, 1987. [6] E.G. Gol'shtein, N.V. Tret'iakov, Modifitsirovannye funktsii Lagranzha, Nauka, M., 1989. [7] A.V. Zhil'tsov, R.V. Namm, “Metod mnozhitelei Lagranzha v zadache konechnomernogo vypuklogo programmirovaniia”, Dal'nevost. matem. zhurn., 15:1, (2015), 53–60. [8] R.V. Namm, E.M. Vikhtenko, Metody vypukloi optimizatsii: uchebnoe posobie, Izd-vo Tikhookean. gos. un-ta, Khabarovsk, 2017. [9] B.T. Poliak, Vvedenie v optimizatsiiu, Nauka, M, 1983. [10] E.M. Vikhtenko, N.N. Maksimova, R.V. Namm, “Funktsionaly chuvstvitel'nosti v variatsionnykh neravenstvakh mekhaniki i ikh prilozhenie k skhemam dvoistvennosti”, Sibirskii zh. vychisl. matem., 17:1, (2014), 43–52. [11] Robert V. Namm, Gyungsoo Woo, “Sensitivity functionals in convex optimization problem”, Filomat, 30:14, (2016), 3681-3687. |