Comparison of advanced large-scale minimization algorithms for the solution of inverse ill-posed problems

References

• Adams , L. M. and Nazareth , J. L. Proceedings of the AMS-IMS-SIAM Summer Research Conference held at the University of Washington . July 1995 . Linear and nonlinear conjugate gradient-related methods , SIAM .
   Google Scholar
• Alekseev , A. K. 2001 . On estimation of entrance boundary parameters from downstream measurements using adjoint approach . Int. J. Numer. Methods Fluids , 36 : 971 – 982 .
   Google Scholar
• Alekseev , A. K. and Navon , I. M. 2001 . The analysis of an ill-posed problem using multiscale resolution and second order adjoint techniques . Comput. Methods Appl. Mech. Eng. , 190 ( 15–17 ) : 1937 – 1953 .
   Web of Science ®Google Scholar
• Alifanov , O. M. , Artyukhin , E. A. and Rumyantsev , S. V. 1996 . Extreme Methods for Solving Ill-posed Problems with Applications to Inverse Heat Transfer Problems , New York, NY : Begell House Inc. Publishers .
   Google Scholar
• Beale , E. M.L. 1972 . “ A derivation of conjugate gradients ” . In Numerical Methods for Nonlinear Optimization , Edited by: Lootsma , F. A. London : Academic Press .
   Google Scholar
• Daescu , D. N. and Navon , I. M. 2003 . An analysis of a hybrid optimization method for variational data assimilation . Int. J. Comput. Fluid Dyn. , 17 ( 4 ) : 299 – 306 .
   Web of Science ®Google Scholar
• Das , B. , Meirovitch , H. and Navon , I. M. 2003 . Performance of enriched methods for large scale unconstrained optimization as applied to models of proteins . J. Comput. Chem. , 24 ( 10 ) : 1222 – 1231 .
   Google Scholar
• Davidon , W. C. 1991 . Variable metric method for minimization . SIAM J. Optim. , 1 : 1 – 17 .
   Web of Science ®Google Scholar
• Dennis , J. E. Jr and More , J. J. 1977 . Quasi-Newton methods, motivation and theory . SIAM Rev. , 19 : 46 – 89 .
   Web of Science ®Google Scholar
• Dennis , J. E. Jr and Schnabel , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , 378 Englewood Cliffs, NJ : Prentice-Hall .
   Google Scholar
• Fletcher , R. and Powell , M. J.D. 1963 . A rapidly convergent descent method for minimization . Comput. J. , 6 : 163 – 168 .
   Web of Science ®Google Scholar
• Gilbert , J. C. 1997 . On the realization of the Wolfe conditions in reduced quasi-Newton methods for equality constrained optimization . SIAM J. Optim. , 7 ( 3 ) : 780 – 813 .
   Google Scholar
• Gilbert , J. C. and Nocedal , J. 1992 . Global convergence properties of conjugate gradient methods . SIAM J. Optim. , 2 : 21 – 42 .
   Web of Science ®Google Scholar
• P.E. Gill and W. Murray, Report SOL 79-15, Department of Operation Research, Stanford University, Stanford, CA, 1979
   Google Scholar
• Gunzburger , M. D. 2000 . Adjoint equation-based methods for control problems in viscous, incompressible flows . Flow Turbul. Comb. , 65 : 249 – 272 .
   Web of Science ®Google Scholar
• Gunzburger , M. D. 2003 . Perspectives in Flow Control and Optimization (Advances in Design and Control) , SIAM .
   Google Scholar
• Hager , W. W. 2000 . Runge–Kutta methods in optimal control and the transformed adjoint system . Numerische Mathematik , 87 ( 2 ) : 247 – 282 .
   Web of Science ®Google Scholar
• Hager , W. W. and Zhang , H. 2005 . A new conjugate gradient method with guaranteed descent and efficient line search . SIAM J. Optim. , 16 ( 1 ) : 170 – 192 .
   Web of Science ®Google Scholar
• Hager , W. W. and Zhang , H. 2006 . Algorithm 851: CG DESCENT, A conjugate gradient method with guaranteed descent . ACM Trans. Math. Softw. , 32 : 113 – 137 .
   Web of Science ®Google Scholar
• Hansen , P. C. 1998 . Rank Deficient and Discrete Ill-posed Problems , 247 Philadelphia : SIAM .
   Google Scholar
• Kelley , C. T. 1999 . Iterative Methods for Optimization , xvi + 180 Philadelphia : SIAM .
   Google Scholar
• Liu , D. C. and Nocedal , J. 1989 . On the limited memory BFGS method for large scale minimization . Math. Program. , 45 : 503 – 528 .
   Web of Science ®Google Scholar
• Morales , J. L. and Nocedal , J. 2002 . Enriched methods for large-scale unconstrained optimization . Comput. Optim. Appl. , 21 : 143 – 154 .
   Web of Science ®Google Scholar
• Morales , J. L. and Nocedal , J. 2000 . Automatic preconditioning by limited memory quasi-Newton updating . SIAM J. Optim. , 10 ( 4 ) : 1079 – 1096 .
   Web of Science ®Google Scholar
• Morales , J. L. and Nocedal , J. 2001 . Algorithm PREQN: FORTRAN subroutines for preconditioning the conjugate gradient method . ACM Trans. Math. Softw. , 27 : 83 – 91 .
   Web of Science ®Google Scholar
• Nash , S. G. 1985 . Preconditioning of truncated Newton methods . SIAM J. Sci. Stat. Comput. , 6 : 599 – 616 .
   Web of Science ®Google Scholar
• Nash , S. G. 1984 . Newton-type minimization via the Lanczos method . SIAM J. Numer. Anal. , 21 : 770 – 788 .
   Web of Science ®Google Scholar
• Nash , S. G. and Nocedal , J. 1991 . A numerical study of the limited memory BFGS method and the truncated-Newton method for large-scale optimization . SIAM J. Optim. , 1 : 358 – 372 .
   Web of Science ®Google Scholar
• Navon , I. M. , Zou , X. , Derber , J. and Sela , J. 1992 . Variational data assimilation with an adiabatic version of the NMC spectral model . Monthly Weather Rev. , 120 ( 7 ) : 1433 – 1446 .
   Web of Science ®Google Scholar
• Nocedal , J. 1992 . Theory of algorithms for unconstrained minimization . Acta Numerica , 1 : 199 – 242 .
   Google Scholar
• Nocedal , J. and Wright , S. J. 1999 . Numerical Optimization , 656 Springer Verlag .
   Google Scholar
• Shanno , D. F. 1978 . Conjugate gradient methods with inexact searches . Math. Oper. Res. , 3 : 244 – 256 .
   Google Scholar
• Shanno , D. F. and Phua , K. H. 1980 . Remark on algorithm 500. Minimization of unconstrained multivariate functions . ACM Trans. Math. Softw. , 6 : 618 – 622 .
   Google Scholar
• Wang , Z. , Navon , I. M. , Zou , X. and LeDimet , F. X. 1995 . A truncated-newton optimization algorithm in meteorology applications with analytic Hessian/vector products . Comput. Opt. Appl. , 4 : 241 – 262 .
   Google Scholar
• Zou , X. , Navon , I. M. , Berger , M. , Phua , K. H. , Schlick , T. and Le Dimet , F. X. 1993 . Numerical experience with limited memory quasi-Newton and truncated Newton methods . SIAM J. Optim. , 3 ( 3 ) : 582 – 608 .
   Google Scholar