Geodesic
Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 10, pp. 1757-1764 Cet article a éte moissonné depuis la source Math-Net.Ru

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An iterative process of the gradient projection type is constructed and examined as a tool for approximating quasisolutions to irregular nonlinear operator equations in a Hilbert space. One step of this process combines a gradient descent step in a finite-dimensional affine subspace and the Fejrér operator with respect to the convex closed set to which the quasisolution belongs. It is proved that the approximations generated by the proposed method stabilize in a small neighborhood of the desired quasisolution, and the diameter of this neighborhood is estimated. 
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A. I. Kozlov; M. Yu. Kokurin. Gradient projection method for stable approximation of quasisolutions to irregular nonlinear operator equations. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 49 (2009) no. 10, pp. 1757-1764. http://geodesic.mathdoc.fr/item/ZVMMF_2009_49_10_a2/

[1] Vasilev F. P., Metody resheniya ekstremalnykh zadach. Zadachi minimizatsii v funktsionalnykh prostranstvakh, regulyarizatsiya, approksimatsiya, Nauka, M., 1981 | MR

[2] Bakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya neregulyarnykh uravnenii, LENAND, M., 2006

[3] Bakushinskii A. B., Goncharskii A. B., Iterativnye metody resheniya nekorrektnykh zadach, Nauka, M., 1989 | MR

[4] Vasin V. V., Eremin I. I., Operatory i iteratsionnye protsessy feierovskogo tipa (teoriya i prilozheniya), RKhD, M.-Izhevsk, 2005 | MR

[5] Vakushinskii A. B., Kokurin M. Yu., Iteratsionnye metody resheniya nekorrektnykh operatornykh uravnenii s gladkimi operatorami, Editorial URSS, M., 2002

[6] Bakushinsky A., Kokurin M., Iterative methods for approximate solution of inverse problems, Springer, Dordrecht, 2005 | MR

[7] Kozlov A. I., “Gradientno-proektsionnyi metod dlya nakhozhdeniya kvazireshenii nelineinykh neregulyarnykh operatornykh uravnenii”, Vychisl. metody i programmirovanie, 4 (2003), 117–125