Nonmonotone globalization of the finite-difference Newton-GMRES method for nonlinear equations

References

• Bellavia , S. , Gasparo , M. G. and Macconi , M. 1996 . A switching-method for nonlinear system . J. Comput. Appl. Math. , 71 : 83 – 93 .
   Google Scholar
• Bertsekas , D. P. 1999 . Nonlinear Programming , 2 Athena Scientific
   Google Scholar
• Bonettini , S. 2005 . A nonmonotone inexact Newton method . Optim. Methods Softw. , 20 : 475 – 491 .
   Web of Science ®Google Scholar
• Brown , A. A. and Bartholomew-Biggs , M. C. 1989 . Some effective methods for unconstrained optimization based on the solution of systems of ordinary differential equations, . J. of Optim. Theory Appl. , 62 : 211 – 224 .
   Web of Science ®Google Scholar
• Brown , P. N. 1987 . A local convergence theory for combined inexact-Newton/ finite difference methods . SIAM J. Numer. Anal. , 24 : 407 – 434 .
   Web of Science ®Google Scholar
• Brown , P. N. and Saad , Y. 1994 . Convergence theory of nonlinear Newton-Krylov algorithms . SIAM J. Optim. , 4 : 297 – 330 .
   Web of Science ®Google Scholar
• Chamberlain , R. M. , Powell , M.J. D. , Lemarechal , C. and Pedersen , H. C. 1982 . The watchdog technique for forcing convergence in algorithms for constrained optimization, . Math. Program. , 16 : 1 – 17 .
   Web of Science ®Google Scholar
• Conn , A. R. , Gould , N.I. M. and Toint , P. L. 2000 . “ MPS-SIAM series on Optimization ” . In Trust-region Methods , Philadelphia : SIAM .
   Google Scholar
• Dembo , R. , Eisenstat , S. C. and Steihaug , T. 1982 . Inexact Newton methods . SIAM J. Numer. Anal. , 19 : 400 – 408 .
   Web of Science ®Google Scholar
• Dennis , J.E. Jr. and Schnabel , R. B. 1983 . Numerical Methods for Unconstrained Optimization and Nonlinear Equations , Englewood Cliffs, NJ : Prentice-Hall, Inc. .
   Google Scholar
• Dennis Jr. , J.E. , Gay , D. M. and Vu , P. A. A new nonlinear equations test problem Rep. 83-16, Rice University, Houston, Texas, 1983, Revised January, 1986
   Google Scholar
• Dirkse , S. P. and Ferris , M. C. 1995 . The PATH solver: A non-monotone stabilization scheme for mixed complementarity problems, . Optim. Methods Softw. , 5 : 123 – 156 .
   Google Scholar
• Eisenstat , S. C. and Walker , H. F. 1994 . Globally convergent inexact Newton methods . SIAM J. Optim. , 4 : 16 – 32 .
   Google Scholar
• Ferris , M. C. and Lucidi , S. 1994 . Nonmonotone stabilization methods for nonlinear equations . J. Optim. Theory Appl. , 81 : 815 – 832 .
   Google Scholar
• Friedlander , A. , Gomes-Ruggiero , M. A. , Kozakevich , D. N. , Martinez , J. M. and Santos , S. A. 1997 . Solving nonlinear systems of equations by means of Quasi-Newton methods with a nonmonotone strategy . Optim. Methods Softw. , 8 : 25 – 51 .
   Web of Science ®Google Scholar
• Gasparo , M. 2000 . A nonmonotone hybrid method for nonlinear systems . Optim. Methods Softw. , 13 : 79 – 84 .
   Web of Science ®Google Scholar
• Gould , N.I. M. , Leyffer , S. and Toint , P. L. 2004 . A multidimensional filter algorithm for nonlinear equations and nonlinear least squares . SIAM J. Optim. , 15 : 17 – 38 .
   Web of Science ®Google Scholar
• Grippo , L. , Lampariello , F. and Lucidi , S. 1986 . A nonmonotone line search technique for Newton’s method . SIAM J. Numer. Anal. , 23 : 707 – 716 .
   Web of Science ®Google Scholar
• Grippo , L. , Lampariello , F. and Lucidi , S. 1988 . Global convergence and stabilization of unconstrained minimization methods without derivatives . J. Optim. Theory Appl. , 56 : 385 – 406 .
   Web of Science ®Google Scholar
• Grippo , L. , Lampariello , F. and Lucidi , S. 1991 . A class of nonmonotone stabilization methods in unconstrained optimization . Numer. Math. , 59 : 779 – 805 .
   Web of Science ®Google Scholar
• Grippo , L. and Sciandrone , M. 2002 . Nonmonotone globalization techniques for the Barzilai-Borwein gradient method . Comput. Optim. Appl. , 23 : 143 – 169 .
   Web of Science ®Google Scholar
• Grippo , L. and Sciandrone , M. 2007 . Nonmonotone derivative-free methods for nonlinear equations . Comput. Optim. Appl. , 27 : 297 – 328 .
   Google Scholar
• Grippo , L. and Sciandrone , M. 2005 . Nonmonotone globalization of inexact finite-difference Newton-iterative methods for nonlinear equations, . Tech. Rep. Dis , n.14
   Google Scholar
• Kelley , C. T. 1995 . Iterative Methods for Linear and Nonlinear Equations , Philadelphia : SIAM .
   Google Scholar
• Kolda , T. G. , Lewis , R. M. and Torczon , V. 2003 . Optimization by direct search: New perspectives on some classical and modern methods . SIAM Rev. , 45 : 385 – 482 .
   Web of Science ®Google Scholar
• Cruz , W. La and Raydan , M. 2003 . Nonmonotone spectral methods for large-scale nonlinear systems . Optim. Methods Softw. , 18 : 583 – 599 .
   Web of Science ®Google Scholar
• Cruz , W. La , Martinez , J. M. and Raydan , M. Spectral residual method without gradient information for solving large-scale nonlinear systems of equations . Tech. Rep. RT-04-08, Dpto. de Computation, UCV, Math. Comp. 75 (2006), pp. 1429–1448
   Google Scholar
• Lewis , R. M. and Torczon , V. 1996 . Rank ordering and positive bases in pattern search algorithms , Institute for Computer Applications in Science and Engineering . Tech. Rep. TR-96-71
   Google Scholar
• Li , D. H. and Fukushima , M. 2000 . A derivative-free line search and global convergence of Broyden-like method for nonlinear equations . Optim. Methods Softw. , 13 : 181 – 201 .
   Web of Science ®Google Scholar
• Li , D. H. , Fukushima , M. , Qi , L. and Yamashita , N. 2004 . Regularized Newton methods for convex minimization problems with singular solutions . Comput. Optim. Appl. , 28 : 131 – 147 .
   Google Scholar
• Lucidi , S. and Sciandrone , M. 2002 . On the global convergence of derivative free methods for unconstrained optimization . SIAM J. Optim. , 13 : 97 – 116 .
   Web of Science ®Google Scholar
• Luksan , L. and Vlcek , J. 1998 . Sparse and partially separable test problems for unconstrained and equality constrained optimization Tech. Rep. V-767, ICS AS CR
   Google Scholar
• Ortega , J. M. and Rheinboldt , W. C. 1970 . Iterative Solution of Nonlinear Equations in Several Variables , Academic Press, New York .
   Google Scholar
• Pawlowski , P. , Shadid , J. N. , Simonis , J. P. and Walker , H. F. 2006 . Globalization techniques for Newton-Krylov methods and applications to the fully coupled solution of the Navier-Stokes equation . SIAM Rev. , 48 : 700 – 721 .
   Web of Science ®Google Scholar
• Pernice , M. and Walker , H. F. 1998 . NITSOL: A Newton iterative solver for nonlinear systems . SIAM J. Sci. Comput. , 19 : 302 – 318 .
   Web of Science ®Google Scholar
• Saad , Y. 2003 . Iterative Methods for Sparse Linear Systems , 2 , Philadelphia : SIAM .
   Google Scholar
• Saad , Y. and Schultz , M. 1986 . GMRES a generalized minimal residual algorithm for solving nonsymmetric linear systems . SIAM J. Sci. Statist. Comput. , 7 : 856 – 869 .
   Web of Science ®Google Scholar
• Toint , Ph. L. 1997 . A non-monotone trust-region algorithm for nonlinear optimization subject to convex constraints . Math. Program. , 77 ( 1 ) : 69 – 94 .
   Google Scholar
• Zhang , H. and Hager , W. W. 2004 . A nonmonotone line search technique and its application to unconstrained optimization . SIAM J. Optim. , 14 : 1045 – 1056 .
   Google Scholar