메뉴 건너뛰기




Volumn 55, Issue 1, 2008, Pages 116-129

A new backtracking inexact BFGS method for symmetric nonlinear equations

Author keywords

BFGS method; Global convergence; Line search; Superlinear convergence; Symmetric nonlinear equations

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; NONLINEAR EQUATIONS; PROBLEM SOLVING; THEOREM PROVING;

EID: 36348953805     PISSN: 08981221     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.camwa.2006.12.081     Document Type: Article
Times cited : (68)

References (22)
  • 1
    • 0001423485 scopus 로고
    • A tool for the analysis of quasi-Newton methods with application to unconstrained minimization
    • Byrd R., and Nocedal J. A tool for the analysis of quasi-Newton methods with application to unconstrained minimization. SIAM Journal on Numerical Analysis 26 (1989) 727-739
    • (1989) SIAM Journal on Numerical Analysis , vol.26 , pp. 727-739
    • Byrd, R.1    Nocedal, J.2
  • 2
    • 0023427318 scopus 로고
    • Global convergence of a class of quasi-Newton methods on convex problems
    • Byrd R., Nocedal J., and Yuan Y. Global convergence of a class of quasi-Newton methods on convex problems. SIAM Journal on Numerical Analysis 24 (1987) 1171-1189
    • (1987) SIAM Journal on Numerical Analysis , vol.24 , pp. 1171-1189
    • Byrd, R.1    Nocedal, J.2    Yuan, Y.3
  • 3
    • 0042659410 scopus 로고    scopus 로고
    • Convergence properties of the BFGS algorithm
    • Dai Y. Convergence properties of the BFGS algorithm. SIAM Journal on Optimization 13 (2003) 693-701
    • (2003) SIAM Journal on Optimization , vol.13 , pp. 693-701
    • Dai, Y.1
  • 6
    • 0000782630 scopus 로고
    • Local convergence analysis for partitioned quasi-Newton updates
    • Griewank A., and Toint Ph.L. Local convergence analysis for partitioned quasi-Newton updates. Numerische Mathematik 39 (1982) 429-448
    • (1982) Numerische Mathematik , vol.39 , pp. 429-448
    • Griewank, A.1    Toint, Ph.L.2
  • 8
    • 0035301251 scopus 로고    scopus 로고
    • A modified BFGS method and its global convergence in nonconvex minimization
    • Li D., and Fukushima M. A modified BFGS method and its global convergence in nonconvex minimization. Journal of Computational and Applied Mathematics 129 (2001) 15-35
    • (2001) Journal of Computational and Applied Mathematics , vol.129 , pp. 15-35
    • Li, D.1    Fukushima, M.2
  • 9
    • 0002340344 scopus 로고
    • A new algorithm for unconstrained optimation
    • Rosen J.B., Mangasarian O.L., and Ritter K. (Eds), Academic Press, New York
    • Powell M.J.D. A new algorithm for unconstrained optimation. In: Rosen J.B., Mangasarian O.L., and Ritter K. (Eds). Nonlinear Programming (1970), Academic Press, New York
    • (1970) Nonlinear Programming
    • Powell, M.J.D.1
  • 11
    • 5544237802 scopus 로고    scopus 로고
    • The superlinear convergence of a modified BFGS-type method for unconstrained optimization
    • Wei Z., Yu G., Yuan G., and Lian Z. The superlinear convergence of a modified BFGS-type method for unconstrained optimization. Computational Optimization and Applications 29 (2004) 315-332
    • (2004) Computational Optimization and Applications , vol.29 , pp. 315-332
    • Wei, Z.1    Yu, G.2    Yuan, G.3    Lian, Z.4
  • 12
    • 33645848452 scopus 로고    scopus 로고
    • New quasi-Newton methods for unconstrained optimization problems
    • Wei Z., Li G., and Qi L. New quasi-Newton methods for unconstrained optimization problems. Applied Mathematics and Computation 175 (2006) 1156-1188
    • (2006) Applied Mathematics and Computation , vol.175 , pp. 1156-1188
    • Wei, Z.1    Li, G.2    Qi, L.3
  • 13
    • 0041740114 scopus 로고
    • The 'global' convergence of Broyden-like methods with a suitable line search
    • Griewank A. The 'global' convergence of Broyden-like methods with a suitable line search. Journal of the Australian Mathematical Society Series B 28 (1986) 75-92
    • (1986) Journal of the Australian Mathematical Society Series B , vol.28 , pp. 75-92
    • Griewank, A.1
  • 14
    • 0039010677 scopus 로고    scopus 로고
    • A global and superlinear convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations
    • Li D., and Fukushima M. A global and superlinear convergent Gauss-Newton-based BFGS method for symmetric nonlinear equations. SIAM Journal on Numerical Analysis 37 (1999) 152-172
    • (1999) SIAM Journal on Numerical Analysis , vol.37 , pp. 152-172
    • Li, D.1    Fukushima, M.2
  • 15
    • 36349000070 scopus 로고    scopus 로고
    • An approximate Gauss-Newton-based BFGS method with descent directions for solving symmetric nonlinear equations
    • Yuan G., and Li X. An approximate Gauss-Newton-based BFGS method with descent directions for solving symmetric nonlinear equations. OR Transactions 8 4 (2004) 10-26
    • (2004) OR Transactions , vol.8 , Issue.4 , pp. 10-26
    • Yuan, G.1    Li, X.2
  • 16
    • 36349030906 scopus 로고    scopus 로고
    • A nonmonotone Gauss-Newton-based BFGS method for solving symmetric nonlinear equations
    • Yuan G., and Lu X. A nonmonotone Gauss-Newton-based BFGS method for solving symmetric nonlinear equations. Journal of Lanzhou University (Natural Sciences) 41 Suppl. (2005) 851-855
    • (2005) Journal of Lanzhou University (Natural Sciences) , vol.41 , Issue.SUPPL , pp. 851-855
    • Yuan, G.1    Lu, X.2
  • 17
    • 10644282908 scopus 로고    scopus 로고
    • Nonmonotone backtracking inexact quasi-Newton algorithms for solving smmoth nonlinear equations
    • Zhu D. Nonmonotone backtracking inexact quasi-Newton algorithms for solving smmoth nonlinear equations. Applied Mathematics and Computation 161 (2005) 875-895
    • (2005) Applied Mathematics and Computation , vol.161 , pp. 875-895
    • Zhu, D.1
  • 18
    • 0000301196 scopus 로고
    • Convergence theorey of nonlinear Newton-Kryloy algorithms
    • Brown P.N., and Saad Y. Convergence theorey of nonlinear Newton-Kryloy algorithms. SIAM Journal on Optimization 4 (1994) 297-330
    • (1994) SIAM Journal on Optimization , vol.4 , pp. 297-330
    • Brown, P.N.1    Saad, Y.2
  • 19
    • 84966259557 scopus 로고
    • A characteization of superlinear convergence and its application to quasi-Newton methods
    • Dennis J.E., and Moré J.J. A characteization of superlinear convergence and its application to quasi-Newton methods. Mathematics of Computation 28 (1974) 549-560
    • (1974) Mathematics of Computation , vol.28 , pp. 549-560
    • Dennis, J.E.1    Moré, J.J.2
  • 20
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • Dennis Jr. J.E., and Moré J.J. Quasi-Newton methods, motivation and theory. SIAM Review 19 (1977) 46-89
    • (1977) SIAM Review , vol.19 , pp. 46-89
    • Dennis Jr., J.E.1    Moré, J.J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.