메뉴 건너뛰기




Volumn 28, Issue 1-2, 2008, Pages 435-446

A modified BFGS method and its superlinear convergence in nonconvex minimization with general line search rule

Author keywords

BFGS algorithm; Global convergence; Non convex function; Quasi Newton method; Unconstrained programme

Indexed keywords


EID: 48749122018     PISSN: 15985865     EISSN: None     Source Type: Journal    
DOI: 10.1007/s12190-008-0117-5     Document Type: Article
Times cited : (13)

References (19)
  • 1
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • 1. J.J. Dennis J.J. Moré 1977 Quasi-Newton methods, motivation and theory SIAM Rev. 19 46 89 0356.65041 10.1137/1019005 445812 Dennis, J.J., Moré, J.J.: Quasi-Newton methods, motivation and theory. SIAM Rev. 19, 46–89 (1977)
    • (1977) SIAM Rev. , vol.19 , pp. 46-89
    • Dennis, J.J.1    Moré, J.J.2
  • 2
    • 0002043221 scopus 로고
    • On the convergence of the variable metric algorithm
    • 2. M.J.D. Powell 1971 On the convergence of the variable metric algorithm J. Inst. Math. Appl. 7 21 36 0217.52804 10.1093/imamat/7.1.21 279977 Powell, M.J.D.: On the convergence of the variable metric algorithm. J. Inst. Math. Appl. 7, 21–36 (1971)
    • (1971) J. Inst. Math. Appl. , vol.7 , pp. 21-36
    • Powell, M.J.D.1
  • 3
    • 0015360954 scopus 로고
    • Variable metric algorithms: necessary and sufficient conditions for identical behavior on nonquadratic functions
    • 3. L.C.W. Dixon 1972 Variable metric algorithms: necessary and sufficient conditions for identical behavior on nonquadratic functions J. Optim. Theory Appl. 10 34 40 0226.49014 10.1007/BF00934961 309305 Dixon, L.C.W.: Variable metric algorithms: necessary and sufficient conditions for identical behavior on nonquadratic functions. J. Optim. Theory Appl. 10, 34–40 (1972)
    • (1972) J. Optim. Theory Appl. , vol.10 , pp. 34-40
    • Dixon, L.C.W.1
  • 4
    • 0023427318 scopus 로고
    • Global convergence of a class of quasi-Newton methods on convex problems
    • 4. R. Byrd J. Nocedal Y. Yuan 1987 Global convergence of a class of quasi-Newton methods on convex problems SIAM J. Numer. Anal. 24 1171 1189 0657.65083 10.1137/0724077 909072 Byrd, R., Nocedal, J., Yuan, Y.: Global convergence of a class of quasi-Newton methods on convex problems. SIAM J. Numer. Anal. 24, 1171–1189 (1987)
    • (1987) SIAM J. Numer. Anal. , vol.24 , pp. 1171-1189
    • Byrd, R.1    Nocedal, J.2    Yuan, Y.3
  • 5
    • 0001423485 scopus 로고
    • A tool for the analysis of quasi-Newton methods with application to unconstrained minimation
    • 5. R. Byrd J. Nocedal 1989 A tool for the analysis of quasi-Newton methods with application to unconstrained minimation SIAM J. Numer. Anal. 26 727 739 0676.65061 10.1137/0726042 997665 Byrd, R., Nocedal, J.: A tool for the analysis of quasi-Newton methods with application to unconstrained minimation. SIAM J. Numer. Anal. 26, 727–739 (1989)
    • (1989) SIAM J. Numer. Anal. , vol.26 , pp. 727-739
    • Byrd, R.1    Nocedal, J.2
  • 6
    • 0027578445 scopus 로고
    • On the global convergence of DFP method
    • 6. D.-H. Li 1993 On the global convergence of DFP method Nat. Sci. J. Hunan Univ. 20 16 20 0774.90064 Li, D.-H.: On the global convergence of DFP method. Nat. Sci. J. Hunan Univ. 20, 16–20 (1993)
    • (1993) Nat. Sci. J. Hunan Univ. , vol.20 , pp. 16-20
    • Li, D.-H.1
  • 7
    • 85121062891 scopus 로고    scopus 로고
    • 7. Powell, M.J.D.: Some global convergence properties of a variable metric algorithm for minimization without exact line searches. In: Cottle, R.W., Lemke C.E. (eds.) Nonlinear Programming, SIAM-AMS Proceedings, vol. 9, pp. 53–72 (1976)
  • 8
    • 0000416096 scopus 로고
    • Uber die global konvergenze von variablemetric verfahren mit nichtexakter schrittweitenbestimmong
    • 8. J. Werner 1978 Uber die global konvergenze von variablemetric verfahren mit nichtexakter schrittweitenbestimmong Numer. Math. 31 321 334 0427.65047 10.1007/BF01397884 514601 Werner, J.: Uber die global konvergenze von variablemetric verfahren mit nichtexakter schrittweitenbestimmong. Numer. Math. 31, 321–334 (1978)
    • (1978) Numer. Math. , vol.31 , pp. 321-334
    • Werner, J.1
  • 9
    • 85121065999 scopus 로고    scopus 로고
    • 9. R. Fletcher 1994 An overview of unconstrained optimization E. Spedicato Algorithms for Continous Optimization: The State of the Art Kluwer Academic Boston 109 143 Fletcher, R.: An overview of unconstrained optimization. In: Spedicato, E. (ed.) Algorithms for Continous Optimization: The State of the Art, pp. 109–143. Kluwer Academic, Boston (1994)
  • 10
    • 21044434499 scopus 로고    scopus 로고
    • The BFGS method with exact line searches fails for non-convex objective functions
    • 10. W.F. Mascarenhas 2004 The BFGS method with exact line searches fails for non-convex objective functions Math. Program. 99 49 61 1082.90108 10.1007/s10107-003-0421-7 2031776 Mascarenhas, W.F.: The BFGS method with exact line searches fails for non-convex objective functions. Math. Program. 99, 49–61 (2004)
    • (2004) Math. Program. , vol.99 , pp. 49-61
    • Mascarenhas, W.F.1
  • 11
    • 4544287790 scopus 로고    scopus 로고
    • Global convergence properties of the modified BFGS method
    • 11. J.G. Liu Q. Guo 2004 Global convergence properties of the modified BFGS method J. Appl. Math. Comput. 16 195 205 1065.65077 2080564 10.1007/BF02936161 Liu, J.G., Guo, Q.: Global convergence properties of the modified BFGS method. J. Appl. Math. Comput. 16, 195–205 (2004)
    • (2004) J. Appl. Math. Comput. , vol.16 , pp. 195-205
    • Liu, J.G.1    Guo, Q.2
  • 12
    • 84949317197 scopus 로고    scopus 로고
    • An modified BFGS method for non-convex minimization problems
    • 12. J.G. Liu Z.Q. Xia R.D. Ge Q. Guo 2004 An modified BFGS method for non-convex minimization problems Oper. Res. Manag. 13 62 65 (Chinese) Liu, J.G., Xia, Z.Q., Ge, R.D., Guo, Q.: An modified BFGS method for non-convex minimization problems. Oper. Res. Manag. 13, 62–65 (2004). (Chinese)
    • (2004) Oper. Res. Manag. , vol.13 , pp. 62-65
    • Liu, J.G.1    Xia, Z.Q.2    Ge, R.D.3    Guo, Q.4
  • 13
    • 0036150486 scopus 로고    scopus 로고
    • An ABS algorithm for solving singular nonlinear system with rank one defect
    • 13. R. Ge Z. Xia 2002 An ABS algorithm for solving singular nonlinear system with rank one defect Korean J. Comput. Appl. Math. 9 167 184 1001.65049 1876521 Ge, R., Xia, Z.: An ABS algorithm for solving singular nonlinear system with rank one defect. Korean J. Comput. Appl. Math. 9, 167–184 (2002)
    • (2002) Korean J. Comput. Appl. Math. , vol.9 , pp. 167-184
    • Ge, R.1    Xia, Z.2
  • 14
    • 0346339447 scopus 로고    scopus 로고
    • An ABS algorithm for solving singular nonlinear system with rank defects
    • 14. R. Ge Z. Xia 2003 An ABS algorithm for solving singular nonlinear system with rank defects J. Appl. Math. Comput. 5 1 20 1976799 Ge, R., Xia, Z.: An ABS algorithm for solving singular nonlinear system with rank defects. J. Appl. Math. Comput. 5, 1–20 (2003)
    • (2003) J. Appl. Math. Comput. , vol.5 , pp. 1-20
    • Ge, R.1    Xia, Z.2
  • 15
    • 0001015017 scopus 로고
    • Variable metric methods of minimization
    • 15. J.D. Pearson 1969 Variable metric methods of minimization Comput. J. 12 171 178 0207.17301 10.1093/comjnl/12.2.171 242355 Pearson, J.D.: Variable metric methods of minimization. Comput. J. 12, 171–178 (1969)
    • (1969) Comput. J. , vol.12 , pp. 171-178
    • Pearson, J.D.1
  • 16
    • 0000115956 scopus 로고
    • General form of stepsize selection rules of linesearch and relevant analysis of global convergence of BFGS algorithm
    • 16. J. Han G. Liu 1995 General form of stepsize selection rules of linesearch and relevant analysis of global convergence of BFGS algorithm Acta Math. Appl. Sin. 1 112 122 1338230 (Chinese) Han, J., Liu, G.: General form of stepsize selection rules of linesearch and relevant analysis of global convergence of BFGS algorithm. Acta Math. Appl. Sin. 1, 112–122 (1995). (Chinese)
    • (1995) Acta Math. Appl. Sin. , vol.1 , pp. 112-122
    • Han, J.1    Liu, G.2
  • 17
    • 84966275544 scopus 로고
    • Minimization of functions having Lipschitz-continuous first partial derivatives
    • 17. L. Armijo 1966 Minimization of functions having Lipschitz-continuous first partial derivatives Pac. J. Math. 16 1 3 0202.46105 191071 Armijo, L.: Minimization of functions having Lipschitz-continuous first partial derivatives. Pac. J. Math. 16, 1–3 (1966)
    • (1966) Pac. J. Math. , vol.16 , pp. 1-3
    • Armijo, L.1
  • 18
    • 0012153097 scopus 로고
    • An effective algorithm for minimization
    • 18. A. Goldstein J. Price 1967 An effective algorithm for minimization Numer. Math. 10 184 189 0161.35402 10.1007/BF02162162 217995 Goldstein, A., Price, J.: An effective algorithm for minimization. Numer. Math. 10, 184–189 (1967)
    • (1967) Numer. Math. , vol.10 , pp. 184-189
    • Goldstein, A.1    Price, J.2
  • 19
    • 0014492147 scopus 로고
    • Convergence conditions for ascent methods
    • 19. P. Wolfe 1969 Convergence conditions for ascent methods SIAM Rev. 11 226 235 0177.20603 10.1137/1011036 250453 Wolfe, P.: Convergence conditions for ascent methods. SIAM Rev. 11, 226–235 (1969)
    • (1969) SIAM Rev. , vol.11 , pp. 226-235
    • Wolfe, P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.