Iterative proximal regularization of a~modified Lagrangian functional for solving a~semicoercive model problem with friction
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 381-396.

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A problem of unconstrained minimization of a semicoercive nondifferentiable functional corresponding to a model friction problem is reduced to a problem of constrained minimization of a differentiable functional. An algorithm based on an iterative proximal regularization of a modified Lagrangian functional is used for solving the problem thus obtained. Convergence of a finite element solution is investigated. The results of numerical calculation are presented.
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     title = {Iterative proximal regularization of a~modified {Lagrangian} functional for solving a~semicoercive model problem with friction},
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N. N. Kushniruk; R. V. Namm. Iterative proximal regularization of a~modified Lagrangian functional for solving a~semicoercive model problem with friction. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 14 (2011) no. 4, pp. 381-396. http://geodesic.mathdoc.fr/item/SJVM_2011_14_4_a3/

[1] Kushniruk N. N., “Metod Udzavy s modifitsirovannoi funktsiei Lagranzha dlya resheniya zadachi o dvizhenii zhidkosti v beskonechnoi trube s treniem na granitse”, Informatika i sistemy upravleniya, 2009, no. 1(19), 3–14

[2] Kushniruk N. N., Namm R. V., “Metod mnozhitelei Lagranzha dlya resheniya polukoertsitivnoi modelnoi zadachi s treniem”, Sib. zhurn. vychisl. matematiki. RAN. Sib. otd-nie, 12:4 (2009), 409–420 | Zbl

[3] Kushniruk N. N., Namm R. V., “Ob odnom podkhode k resheniyu polukoertsitivnoi modelnoi zadachi s treniem”, Dalnevostochnyi matem. zhurn., 8:2 (2008), 171–179 | MR

[4] Glovinski R., Lions Zh.-L., Tremoler R., Chislennoe issledovanie variatsionnykh neravenstv, Mir, M., 1979 | MR

[5] Namm R. V., “O edinstvennosti gladkogo resheniya v statisticheskoi zadache s treniem po zakonu Kulona i dvustoronnim kontaktom”, Prikladnaya matematika i mekhanika, 59:2 (1995), 330–335 | MR | Zbl

[6] Golshtein E. G., Tretyakov N. V., Modifitsirovannye funktsii Lagranzha. Teoriya i metody optimizatsii, Nauka, M., 1989 | MR

[7] Bertsekas D. P., Nonlinear Programming, Athena Scientific, Belmont–Massachusetts, 1999 | Zbl

[8] Vu G., Kim S., Namm R. V., Sachkov S. A., “Metod iterativnoi proksimalnoi regulyarizatsii dlya poiska sedlovoi tochki v polukoertsitivnoi zadache Sinorini”, Zhurn. vychisl. matem. i mat. fiziki, 46:11 (2006), 2024–2031 | MR

[9] Antipin A. S., Metody nelineinogo programmirovaniya, osnovannye na pryamoi i dvoistvennoi modifikatsii funktsii Lagranzha, Preprint, VNII sistemnykh issledovanii, Moskva, 1979

[10] Bertsekas D., Uslovnaya optimizatsiya i metody mnozhitelei Lagranzha, Radio i svyaz, M., 1987 | MR | Zbl

[11] Grossman K., Kaplan A. A., Nelineinoe programmirovanie na osnove bezuslovnoi optimizatsii, Nauka. Sibirskoe otd-nie, Novosibirsk, 1981 | Zbl

[12] Kushniruk N. N., Optimizatsionnye metody resheniya variatsionnykh neravenstv, Dis. $\dots$ kand. fiz.-mat. nauk., Khabarovsk, 2010

[13] Grisvard P., Boundary Value Problems in Non-Smooth Domains, Univ. Dept. Math. College Park, Maryland, MD, 1980

[14] Syarle F., Metod konechnykh elementov dlya ellipticheskikh zadach, Mir, M., 1980 | MR

[15] Glavachek I., Gaslinger Ya., Nechas I., Lovishek Ya., Reshenie variatsionnykh neravenstv v mekhanike, Mir, M., 1986 | MR

[16] Marchuk G. I., Agoshkov V. I., Vvedenie v proektsionno-setochnye metody, Nauka, M., 1981 | MR | Zbl

[17] Khludnev A. M., Zadachi teorii uprugosti v negladkikh oblastyakh, Fizmatlit, M., 2010

[18] Kovtunenko V. A., “Variatsionnaya i kraevaya zadachi s treniem na vnutrennei granitse”, Sibirskii matem. zhurn., 39:5 (1998), 1060–1073 | MR | Zbl

[19] Christensen P. W., Klarbring A., Pang J. S., Stroemberg N., “Formulation and comparison of algorithms for frictional contact problems”, Int. J. Numer. Meth. Eng., 42 (1998), 145–173 | 3.0.CO;2-L class='badge bg-secondary rounded-pill ref-badge extid-badge'>DOI | MR | Zbl

[20] Kazufumi Ito, Karl Kunisch, “Augmented Lagrangian methods for nonsmoth, convex optimization in Hilbert space”, Nonlinear Analysis, 41 (2000), 591–616 | DOI | MR | Zbl

[21] Kunusch K., Stadler G., “Generalized Newton methods for the 2D-Signorini contact problem with friction in function space”, Math. Modeling Numer. Anal., 39 (2005), 827–854 | DOI | MR