Levenberg–Marquardt methods with strong local convergence properties for solving nonlinear equations with convex constraints

Journal of Computational and Applied Mathematics - Tập 172 Số 2 - Trang 375-397 - 2004
Christian Kanzow1, Nobuo Yamashita2, Masao Fukushima2
1Institute of Applied Mathematics and Statistics, University of Würzburg, Am Hubland, 97074 Würzburg, Germany
2Department of Applied Mathematics and Physics, Graduate School of Informatics, Kyoto University, Kyoto 606-8501, Japan

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Bellavia, 2003, An affine scaling trust-region approach to bound-constrained nonlinear systems, Appl. Numer. Math, 44, 257, 10.1016/S0168-9274(02)00170-8

S. Bellavia, M. Macconi, B. Morini, STRSCNE: a scaled trust-region solver for constrained nonlinear systems, Comput. Optim. Appl., to appear.

Bertsekas, 1995

Dan, 2002, Convergence properties of the inexact Levenberg–Marquardt method under local error bound conditions, Optim. Methods Software, 17, 605, 10.1080/1055678021000049345

Dennis, 1983

Deuflhard, 1991

Dirkse, 1995, MCPLIB, Optim. Methods Software, 5, 319, 10.1080/10556789508805619

J.Y. Fan, Y.X. Yuan, On the convergence of a new Levenberg–Marquardt method, Technical Report, AMSS, Chinese Academy of Sciences, Beijing, China, 2001.

C.A. Floudas, P.M. Pardalos, C.S. Adjiman, W.R. Esposito, Z.H. Gumus, S.T. Harding, J.L. Klepeis, C.A. Meyer, C.A. Schweiger, Handbook of Test Problems in Local and Global Optimization, Nonconvex Optimization and Its Applications, Vol. 33, Kluwer Academic Publishers, The Netherlands, 1999.

Gabriel, 1994, A trust region method for constrained nonsmooth equations, 155

Hock, 1981, Test Examples for Nonlinear Programming Codes, Vol. 187

Hoffman, 1952, On approximate solutions of systems of linear inequalities, J. Nat. Bur. Stand, 49, 263, 10.6028/jres.049.027

Kanzow, 2001, An active set-type Newton method for constrained nonlinear systems, 179

Kanzow, 2001, Strictly feasible equation-based methods for mixed complementarity problems, Numer. Math, 89, 135, 10.1007/PL00005460

Kelley, 1995

Kozakevich, 1997, Solving nonlinear systems of equations with simple bounds, Comput. Appl. Math, 16, 215

Meintjes, 1987, A methodology for solving chemical equilibrium systems, Appl. Math. Comput, 22, 333

Meintjes, 1990, Chemical equilibrium systems as numerical test problems, ACM Trans. Math. Software, 16, 143, 10.1145/78928.78930

Monteiro, 1999, A potential reduction Newton method for constrained equations, SIAM J. Optim, 9, 729, 10.1137/S1052623497318980

Ortega, 1970

L. Qi, X.-J. Tong, D.-H. Li, An active-set projected trust region algorithm for box constrained nonsmooth equations, J. Optim. Theory Appl., to appear.

Robinson, 1981, Some continuity properties of polyhedral multifunctions, Math. Programming Stud, 14, 206, 10.1007/BFb0120929

Ulbrich, 2001, Nonmonotone trust-region method for bound-constrained semismooth equations with applications to nonlinear mixed complementarity problems, SIAM J. Optim, 11, 889, 10.1137/S1052623499356344

Wang, 1996, An interior point potential reduction method for constrained equations, Math. Programming, 74, 159, 10.1007/BF02592210

Yamashita, 2001, On the rate of convergence of the Levenberg–Marquardt method, Comput, 15, 239