A regularized method for solving constrained pseudoinverse problems
- 21 Downloads
For a constrained pseudoinverse problem whose operators satisfy the complementarity condition we propose a one-parameter continuous regularization method of the second order. This method is based on stabilization of solutions to Cauchy problems for a linear differential equation of the second order in a Hilbert space which is obtained from the heavy ball method. We establish requirements to the parametric regularization function and perturbation levels that ensure the stability of the method in the class of all possible bounded perturbations.
Keywordsconstrained pseudoinverse problem continuous regularization method of second order complementarity condition for operators
Unable to display preview. Download preview PDF.
- 2.Morozov, V. A. and Kirsanova, N. N. “One Generalization of the Regularization Method” in Calculating Methods and Programming (Mosk. Gos. Univ., Moscow, 1970), No. 14, 40–45.Google Scholar
- 5.Vainikko, G. M. and Veretennikov, A. Yu. Iteration Procedures in Ill-Posed Problems (Nauka, Moscow, 1986) [in Russian].Google Scholar
- 8.Bondar’, E. A. and Shafiev, R. A. “Solution of a Constrained Pseudoinversion Problem by the Second Order Continuous RegularizationMethod”, Vestn.NGGU.Matem.Modelir. iOptim. Upravlenie, No. 11, 176–182 (2011) [in Russian].Google Scholar
- 11.Bondar’, E. A. and Yastrebova, I. Yu. “Setting Method for Constrained Pseudoinversion Problem”, Vestn. NGGU.Matem.Modelir. i Optim. Upravlenie 1, 55–63 (2003) [in Russian].Google Scholar
- 12.Bondar’, E. A. and Shafiev, R. A. “A Continuous Method for Solving the Constrained Pseudoinverse Problem”, Vestn. NGGU.Matematika 1, 4–14 (2006).Google Scholar
- 13.Shafiev, R. A., Bondar’, E. A., and Yastrebova, I. Yu. “A Continuous RegularizationMethod and Constrained Pseudoinversion Problems with Additional Restrictions on Input Operators”, Uchen. Zap. Kazansk. Univ. Ser. Fiz.-Matem. Nauki 158, No. 1, 106–116 (2016) [in Russian].Google Scholar
- 14.Antipin, A. S. “Continuous and Iterative Processeswith Projection and Projection-TypeOperators“, Voprosy Kibernetiki. Vychisl. Vopr. Analiza Bol’shikh Sistem (Nauchn. sovet po kompleksnoi probleme “Kibernetika ” Akad. Nauk SSSR, Moscow, 1989), pp. 5–43 [in Russian].Google Scholar
- 15.Vasil’ev, F. P. Methods for Solving Extremum Problems (Nauka, Moscow, 1981) [in Russian].Google Scholar