MODIFIED LIMITED MEMORY BFGS METHOD WITH NONMONOTONE LINE SEARCH FOR UNCONSTRAINED OPTIMIZATION

키워드

참고문헌 (51)

1. C. G. Broyden, "On the local and superlinear convergence of quasi-Newton methods", J. Inst. Math. Appl., 12, pp.223~245 (1973)
2. R. H. Byrd, "A tool for the analysis of quasi-Newton methods with application to unconstrained minimization", SIAM J. Numer. Anal., 26(3), pp.727~739 (1989)
3. R. H. Byrd, "Representations of quasi-Newton matrices and their use in limited memory methods", Math. Programming, 63(2), pp.129~156 (1994)
4. R. Byrd, "Global convergence of a class of quasi-Newton methods on convex problems", SIAM J. Numer. Anal., 24(5), pp.1171~1190 (1987)
5. Y. Dai, "Convergence properties of the BFGS algorithm", SIAM J. Optim., 13(3), pp.693~701 (2002)
6. Y. Dai, "Testing different conjugate gradient methods for large-scale unconstrained optimization", J. Comput. Math., 21(3), pp.311~320 (2003)
7. Variable metric methods for minimization, "W. C. Davidon", ~, pp.A. E. C. Research and Development Report ANL-599 (1959)
8. R. Dembo, "Truncated Newton algorithms for large-scale unconstrained optimization", Math. Programming, 26(2), pp.190~212 (1983)
9. J. E. Dennis Jr., "Quasi-Newton methods, motivation and theory", SIAM Rev., 19(1), pp.46~89 (1977)
10. J. E. Dennis Jr., "A characterization of superlinear convergence and its application to quasi-Newton methods", Math. Comp., 28, pp.549~560 (1974)
11. J. E. Dennis Jr., "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" (1983), Prentice Hall, Inc.
12. L. C. W. Dixon, "Variable metric algorithms: necessary and sufficient conditions for identical behavior of nonquadratic functions", J. Optimization Theory Appl., 10, pp.34~40 (1972)
13. E. D. Dolan, "Benchmarking optimization software with performance profiles", Math. Program. Ser. A, 91(2), pp.201~213 (2002)
14. R. Fletcher, "Practical Methods of Optimization, Second edition" (1987), A Wiley-Interscience Publication. John Wiley & Sons, Ltd.
15. N. I. M. Gould, "CUTEr (and SifDec), a constrained and unconstrained testing environment, revisite", ACM Transactions on Mathematical Software, 29, pp.373~394 (2003)
16. A. Griewank, "The global convergence of partitioned BFGS on problems with convex decompositions and Lipschitzian gradients", Math. Programming(Ser. A), 50(2), pp.141~175 (1991)
17. A. Griewank, "Local convergence analysis for partitioned quasi-Newton updates", Numer. Math., 39(3), pp.429~448 (1982)
18. L. Grippo, "A nonmonotone line search technique for Newton’s method", SIAM J. Numer. Anal., 23(4), pp.707~716 (1986)
19. L. Grippo, "A truncated Newton method with nonmonotone line search for unconstrained optimization", J. Optim. Theory Appl., 60(3), pp.401~419 (1989)
20. L. Grippo, "A class of nonmonotone stabilization methods in unconstrained optimization", Numer. Math., 59(8), pp.779~805 (1991)
21. J. Y. Han, "Global convergence analysis of a new nonmonotone BFGS algorithm on convex objective functions", Comput. Optim. Appl., 7(3), pp.277~289 (1997)
22. D. Li, "A modified BFGS method and its global convergence in nonconvex minimization", J. Comput. Appl. Math., 129(1), pp.15~35 (2001)
23. D. Li, "On the global convergence of the BFGS method for nonconvex unconstrained optimization problems", SIAM J. Optim., 11(4), pp.1054~1064 (2001)
24. G. Li, "New conjugacy condition and related new conjugate gradient methods for unconstrained optimization", J. Comput. Appl. Math., 202(2), pp.523~539 (2007)
25. G. H. Liu, "Notes on the general form of stepsize selection", OR and Decision Making, 1, pp.619~624 (1992)
26. Global convergence Analysis of the variable metric algorithm with a generalized Wolf linesearch, Technical Report, "G. H. Liu", Institute of Applied Mathematics, ~, pp.Academia Sinica, Beijing, China, no. 029 (1993)
27. G. H. Liu, "Global convergence of the BFGS algorithm with nonmonotone linesearch", Optimization, 34(2), pp.147~159 (1995)
28. G. H. Liu, "The convergence properties of a nonmonotonic algorithm", J. Comput. Math., 1, pp.65~71 (1992)
29. W. F. Mascarenhas, "The BFGS method with exact line searches fails for non-convex objective functions", Math. Program. Ser. A, 99(1), pp.49~61 (2004)
30. J. J. Mor´e, "Testing unconstrained optimization software", ACM Trans. Math. Software, 7(1), pp.17~41 (1981)
31. S. G. Nash, "A survey of truncated-Newton methods, Numerical analysis 2000, Vol. IV, Optimization and nonlinear equations", J. Comput. Appl. Math., 124(1), pp.45~59 (2000)
32. M. J. D. Powell, "On the convergence of the variable metric algorithm", J. Inst. Math. Appl., 7, pp.21~36 (1971)
33. M. J. D. Powell, "Some global convergence properties of a variable metric algorithm for minimization without exact line searches, Nonlinear programming", SIAM-AMS Proc., 통권 : 11, pp.53~72 (1976), Amer. Math. Soc.
34. M. J. D. Powell, "A new algorithm for unconstrained optimization, 1970 Nonlinear Programming", Proc. Sympos., pp.31~65 (1970), Academic Press
35. M. Raydan, "The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem", SIAM J. Optim., 7(1), pp.26~33 (1997)
36. J. Schropp, "A note on minimization problems and multistep methods", Numer. Math., 78(1), pp.87~101 (1997)
37. J. Schropp, "One-step and multistep procedures for constrained minimization problems", IMA J. Numer. Anal., 20(1), pp.135~152 (2000)
38. Ph. L. Toint, "Global convergence of the partitioned BFGS algorithm for convex partially separable optimization", Math. Programming, 36(3), pp.290~306 (1986)
39. D. J. van Wyk, "Differential optimization techniques", Appl. Math. Modelling, 8(6), pp.419~424 (1984)
40. M. N. Vrahatis, "A class of gradient unconstrained minimization algorithms with adaptive stepsize", J. Comput. Appl. Math., 114(2), pp.367~386 (2000)
41. Z. Wei, "New quasi-Newton methods for unconstrained optimization problems", Appl. Math. Comput., 175(2), pp.1156~1188 (2006)
42. Z. Wei, "The superlinear convergence of a modified BFGStype method for unconstrained optimization", Comput. Optim. Appl., 29(3), pp.315~332 (2004)
43. G. L. Yuan, "Modified nonlinear conjugate gradient methods with sufficient descent property for large-scale optimization problems", Optim. Lett., 3(1), pp.11~21 (2009)
44. G. L. Yuan, "A new line search method with trust region for unconstrained optimization", Comm. Appl. Nonlinear Anal., 15(1), pp.35~49 (2008)
45. G. L. Yuan, "A modified PRP conjugate gradient method", Ann. Oper. Res., 166, pp.73~90 (2009)
46. G. L. Yuan, "A conjugate gradient method with descent direction for unconstrained optimization", J. Comput. Appl. Math., 233(2), pp.519~530 (2009)
47. Y. Yuan, "Theory and Methods of Optimization" (1999), Science Press of China
48. Gonglin Yuan, "New line search methods for unconstrained optimization", Journal of the Korean Statistical Society, 38(1), pp.29~39 (2009), 한국통계학회
49. G. L. Yuan, "The superlinear convergence analysis of a nonmonotone BFGS algorithm on convex objective functions", Acta Math. Sin. (Engl. Ser.), 24(1), pp.35~42 (2008)
50. G. L. Yuan, "Convergence analysis of a modified BFGS method on convex minimizations", Comput. Optim. Appl.
51. J. Z. Zhang, "New quasi-Newton equation and related methods for unconstrained optimization", J. Optim. Theory Appl., 102(1), pp.147~167 (1999)

관련 논문AI추천