Some iterative regularized methods for highly nonlinear least squares problems

References

• Bakushinskij , A.B. and Kokurin , M.Y. 2004 . Iterative Methods for Approximate Solution of Inverse Problems , Springer .
   Google Scholar
• Bakushinskij , A.B. and Polyak , B.T. 1974 . On solving variational inequalities . DAN SSSR, , 219 : 1038 – 1041 . (in Russian)
   Google Scholar
• Chen , J. 2008 . The convergence analysis of inexact Gauss‐Newton methods for nonlinear problems . Computational Optimization and Applications, , 40 (1) : 97 – 118 .
   Web of Science ®Google Scholar
• Čiegis , R. , Ilgevičius , A. , Jankevičiūt?e , G. and Meilūnas , M. 2009 . Determination of heat conductivity coefficient of a cable bundle by inverse problem solution method . Electronics and Electronical Engineering, , 2 (90) : 77 – 80 .
   Google Scholar
• Čiegis , Raim. , Čiegis , Rem. , Meilūnas , M. , Jankevičiūt?e , G. and Starikovičius , V. 2008 . Parallel numerical algorithms for optimization of electrical cables . Math. Model. Anal., , 13 (4) : 471 – 482 . (doi:10.3846/1392–6292.2008.13.471–482)
   Web of Science ®Google Scholar
• Domanskij , E. 1994 . Sequential regularizability in the sense of Maslov for improperly posed problems . Mathematical Notes, , 4 : 1036 – 1042 .
   Google Scholar
• Guseinov , S. and Buikis , A. 2002 . Inverse heat transport problems for coeffcients in two‐layer domains and methods for their solution . Math. Model. Anal., , 7 (2) : 217 – 228 .
   Google Scholar
• Kaltenbacher , B. and Neubauer , A. 2006 . Convergence of projected iterative regularization methods for nonlinear problems with smooth solutions . Inverse problems, , 22 : 1105 – 1119 .
   Web of Science ®Google Scholar
• Kaltenbacher , B. , Neubauer , A. and Scherzer , O. 2008 . Iterative Regularization Methods for Nonlinear Ill‐Posed Problems , Walter de Gruyter .
   Google Scholar
• Kamkamidze , K. and Nemsadze , A. 2004 . Application of neural networks for short‐term forecasting of electric system's load . Proc. of the Intern. Scientific Conference Problems of Control and Power Engineering . 2004 , Tbilisi, Georgia. pp. 252 – 256 . Georgian Academy of Sciences, 2004. A. Eliashvili Institute of Control Systems . (in Russian)
   Google Scholar
• Kangro , I. and Vaarmann , O. The 20th Inter. Conference EurOPT'2008, Selected papers, Neringa, Lithuania, 2008 . Continuous Optimization and Knowledge‐Based Technologies . Two‐parameter regularized Gauss‐Newton type methods for highly nonlinear least squares problems , Edited by: Sakalauskas , L. pp. 160 – 164 . Institute of Mathematics and Informatics, 2008. VGTU Publishing House . “Technica”
   Google Scholar
• Natterer , F. 2001 . The Mathematics of Computerized Tomography , SIAM .
   Google Scholar
• Pais , E. and Janno , J. 2006 . Inverse problem to determine degenerate memory kernels in heat flux with third kind boundary conditions . Math. Model. Anal., , 11 (4) : 427 – 450 .
   Google Scholar
• Parts , I. and Vaarmann , O. 2006 . Intern. Conference on Operational Research SOBI2006 . Simulation and Optimisation in Business and Industry . 2006 , Tallinn, Estonia. Damped Gauss‐Newton type methods for ill‐posed optimization problems , Edited by: Pranevicius , H. pp. 119 – 123 . Kaunas University of Technology . 2006. Technologija, Kaunas
   Google Scholar
• Petlenkov , E. 2007 . Neural Networks Based Identification and Control of Nonlinear Systems: ANARX Model Based Approach. , Tallinn : Tallinn University of Technology . (Ph.D thesis)
   Google Scholar
• Qi‐Nian , J. 2000 . On the iteratively regularized Gauss‐Newton method for solving nonlinear ill‐posed problems . Math. Computation, , 69 (232) : 1603 – 1623 .
   Web of Science ®Google Scholar
• Qinian , J. 2008 . A convergence analysis of the iteratively regularized Gauss‐Newton method under the Lipschitz condition . Inverse problems , 24 : 16 045002
   Web of Science ®Google Scholar
• Rudnicki , M. , Czczepaniak , P.S. and Cholajda , R. 1999 . “ Genetic algorithm as a tool for solving electrical engineering problems ” . In Evolutionary Algorithms in Engineering and Computer Science , Edited by: Mietinen , K. 261 – 281 . John Wiley & Sons, Inc. .
   Google Scholar
• Sipra , B. 1997 . Application of optimization. The best of all possible worlds . SIAM NEWS, , 30 (2)
   Google Scholar
• Smirnova , A.V. 1992 . Discretization and iterative approximation of solutions for nonlinear ill‐posed problems . Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, , 8 : 73 – 79 . (in Russian)
   Google Scholar
• Vaarmann , O. 1989 . Solution of nonlinear least squares problems by Levenberg‐Marquardt type methods . Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, , 38 (2) : 146 – 153 .
   Google Scholar
• Vaarmann , O. 1994 . On solving ill‐conditioned systems of nonlinear equations . Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, , 43 (2) : 49 – 63 .
   Google Scholar
• Vaarmann , O. 1999 . Some approximate methods for ill‐posed problems . Proceedings of the Estonian Academy of Sciences: Physics, Mathematics, , 48 (2) : 146 – 151 .
   Google Scholar
• Vainikko , G. and Hämarik , U. 1985 . Projection methods and self‐regularization in ill‐posed problems . Soviet Mathematics, , 29 : 1 – 20 .
   Google Scholar
• Vasin , V. 1995 . Iterative regularization techniques for ill‐posed problems . Russian Mathematics (Iz. VUZ), , 11 : 69 – 84 .
   Google Scholar
• Vasin , V.V. and Mokrushin , A.A. 2000 . Iterative process of Gauss‐Newton type for ill‐posed operator equations . Dokl. Akad. Nauk., , 371 (1) : 35 – 37 .
   Web of Science ®Google Scholar
• This work was partly supported by Estonian Scientific Competence Council targeted financing grant no. 0140083s08
   Google Scholar