Steepest descent preconditioning for nonlinear GMRESoptimization

Numerical Linear Algebra with Applications

Volumn 20, Issue 3, 2013, Pages 453-471

  De Sterck, Hans ^a  

^a UNIVERSITY OF WATERLOO   (Canada)

Author keywords

BFGS method; Conjugate gradient method; GMRES; Nonlinear optimization; Preconditioning; Steepest descent

Indexed keywords

EID: 84876784628     PISSN: 10705325     EISSN: 10991506     Source Type: Journal    
DOI: 10.1002/nla.1837     Document Type: Article

References (18)

1. De Sterck H.A nonlinear GMRES optimization algorithm for canonical tensor decomposition. SIAM Journal on Scientific Computing accepted 2012. arXiv:1105.5331.
2. Nocedal J, Wright SJ.Numerical Optimization, 2nd ed. Springer: Berlin, 2006.
3. Washio T, Oosterlee CW.Krylov subspace acceleration for nonlinear multigrid schemes. Electronic Transactions on Numerical Analysis 1997; 6:271-290.
4. Oosterlee CW, Washio T.Krylov subspace acceleration of nonlinear multigrid with application to recirculating flows. SIAM Journal on Scientific Computing 2000; 21:1670-1690.
5. Oosterlee CW.On multigrid for linear complementarity problems with application to American-style options. Electronic Transactions on Numerical Analysis 2003; 15:165-185.
6. Saad Y, Schultz MH.GMRES: A generalized minimal residual algorithm for solving nonsymmetric linear systems. SIAM Journal on Scientific Computing 1986; 7:856-869.
7. Saad Y.Iterative Methods for Sparse Linear Systems, 2nd ed. SIAM: Philadelphia, 2003.
8. Saad Y.A flexible inner-outer preconditioned GMRES algorithm. SIAM Journal on Scientific Computing 1993; 14:461-469.
9. Smith DA, Ford WF, Sidi A.Extrapolation methods for vector sequences. SIAM Review 1987; 29:199-234.
10. Fang H, Saad Y.Two classes of multisecant methods for nonlinear acceleration. Numerical Linear Algebra with Applications 2009; 16:197-221.
11. Walker H, Ni P.Anderson acceleration for fixed-point iterations. SIAM Journal on Numerical Analysis 2011; 49:1715-1735.
12. Gilbert JC, Nocedal J.Global convergence properties of conjugate gradient methods for optimization. SIAM Journal on Optimization 1992; 2:21-42.
13. Moré JJ, Thuente DJ.Line search algorithms with guaranteed sufficient decrease. ACM Transactions on Mathematical Software 1994; 20:286-307.
14. Dunlavy DM, Kolda TG, Acar E.Poblano v1.0: A MATLAB Toolbox for Gradient-Based Optimization. Technical Report SAND2010-1422, Sandia National Laboratories, Albuquerque, NM and Livermore, CA, March 2010.
15. Moré JJ, Garbow BS, Hillstrom KE.Testing unconstrained optimization software. ACM Transactions on Mathematical Software 1981; 7:17-41.
16. Acar E, Dunlavy DM, Kolda TG.A scalable optimization approach for fitting canonical tensor decompositions. Journal of Chemometrics 2011; 25:67-86.
17. Bader BW, Kolda TG.MATLAB Tensor Toolbox Version 2.4. http://csmr.ca.sandia.gov/ tgkolda/TensorToolbox [March 2010].
18. Hager WW, Zhang H.A survey of nonlinear conjugate gradient methods. Pacific Journal of Optimization 2006; 2:35-58.