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Volumn 15, Issue 1, 2008, Pages 35-49

A new line search method with trust region for unconstrained optimization

Author keywords

Global convergence; Line search method; Trust region; Unconstrained optimization

Indexed keywords


EID: 40249107806     PISSN: 1074133X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (11)

References (37)
  • 1
    • 0001423485 scopus 로고
    • A tool for the analysis of quasi-Newton methods with application to unconstrained minimization
    • R. Byrd and J. Nocedal, 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
  • 3
    • 0042659410 scopus 로고    scopus 로고
    • Convergence properties of the BFGS algorithm
    • Y. Dai, 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
  • 4
    • 40249108350 scopus 로고    scopus 로고
    • Y. Dai, A nonmonotone conjugate gradient algorithm for unconstrained optimization, J. Syst. Sci. Complex., 15(2002), 139-145.
    • Y. Dai, A nonmonotone conjugate gradient algorithm for unconstrained optimization, J. Syst. Sci. Complex., 15(2002), 139-145.
  • 5
    • 0033266804 scopus 로고    scopus 로고
    • A nonlinear conjugate gradient with a strong global convergence properties
    • Y. Dai and Y. Yuan, A nonlinear conjugate gradient with a strong global convergence properties, SIAM Journal of Optimization, 10(2000), 177-182.
    • (2000) SIAM Journal of Optimization , vol.10 , pp. 177-182
    • Dai, Y.1    Yuan, Y.2
  • 7
    • 84966259557 scopus 로고
    • A characteization of superlinear convergence and its application to quasi-Newton methods
    • J. E. Dennis and J. J. Moré, A characteization of superlinear convergence and its application to quasi-Newton methods, Math. Comp., 28 (1974), 549-560.
    • (1974) Math. Comp , vol.28 , pp. 549-560
    • Dennis, J.E.1    Moré, J.J.2
  • 8
    • 0002663672 scopus 로고
    • Quasi-Newton methods, motivation and theory
    • J. E. Dennis Jr., J. J. Moré, Quasi-Newton methods, motivation and theory, SIAM Rev., 19(1977), 46-89.
    • (1977) SIAM Rev , vol.19 , pp. 46-89
    • Dennis Jr., J.E.1    Moré, J.J.2
  • 9
    • 0742266953 scopus 로고    scopus 로고
    • A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations
    • J. Y. Fan, A modified Levenberg-Marquardt algorithm for singular system of nonlinear equations, J. Comput. Math., 21(2003), 625-636.
    • (2003) J. Comput. Math , vol.21 , pp. 625-636
    • Fan, J.Y.1
  • 10
    • 12444278220 scopus 로고    scopus 로고
    • Nonmonotone adaptive trust-region method for unconstrained optimization problems
    • J. H. Fu and W. Y. Sun, Nonmonotone adaptive trust-region method for unconstrained optimization problems, Applied Mathematics and Computation, 163(2005), 489-504.
    • (2005) Applied Mathematics and Computation , vol.163 , pp. 489-504
    • Fu, J.H.1    Sun, W.Y.2
  • 11
    • 0003333302 scopus 로고    scopus 로고
    • Practical Method of Optimization
    • 2nd edition, Wiley, New York
    • R. Fletcher, Practical Method of Optimization, Vol I: Unconstrained Optimization, 2nd edition, Wiley, New York, 1997.
    • (1997) Unconstrained Optimization , vol.1
    • Fletcher, R.1
  • 12
    • 0000615669 scopus 로고
    • Function minimization bu conjugate gradients
    • R. Fletcher and C. Reeves, Function minimization bu conjugate gradients, Compute. J., 7(1964), 149-154.
    • (1964) Compute. J , vol.7 , pp. 149-154
    • Fletcher, R.1    Reeves, C.2
  • 13
    • 0000782630 scopus 로고
    • Local convergence analysis for partitioned quasi-Newton updates
    • A. Griewank and Ph. L. Toint, Local convergence analysis for partitioned quasi-Newton updates. Numer. Math., 39(1992), 429-448.
    • (1992) Numer. Math , vol.39 , pp. 429-448
    • Griewank, A.1    Toint, P.L.2
  • 14
    • 0000135303 scopus 로고
    • Method Of Conjugate gradient for solving linear equations
    • M. R. Hestenes and E. Stiefel, Method Of Conjugate gradient for solving linear equations, J, Res. Nat. Bur. Stand., 49(1952), 409-436.
    • (1952) J, Res. Nat. Bur. Stand , vol.49 , pp. 409-436
    • Hestenes, M.R.1    Stiefel, E.2
  • 16
    • 0035301251 scopus 로고    scopus 로고
    • A modified BFGS method and its global convergence in non-convex minimization
    • D. Li and M. Fukushima, A modified BFGS method and its global convergence in non-convex 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
  • 17
    • 40249085707 scopus 로고
    • Effcient generalized conjugate gradient algorithms, part 1: Theory
    • Y. Liu and C. Storey, Effcient generalized conjugate gradient algorithms, part 1: theory, Journal of optimization theory and Application, 69(1992), 17-41.
    • (1992) Journal of optimization theory and Application , vol.69 , pp. 17-41
    • Liu, Y.1    Storey, C.2
  • 22
    • 0002340344 scopus 로고
    • A new algorithm for unconstrained optimation
    • J. B. Rosen, O.L.Mangasarian and K.Ritter, eds. Academic Press, New York
    • M. J. D Powell, A new algorithm for unconstrained optimation, In: Nonlinear Programming, J. B. Rosen, O.L.Mangasarian and K.Ritter, eds. Academic Press, New York, 1970.
    • (1970) Nonlinear Programming
    • Powell, M.J.D.1
  • 23
    • 0031542191 scopus 로고    scopus 로고
    • The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem
    • M. Raydan, The Barzilai and Borwein gradient method for the large scale unconstrained minimization problem, SIAM J. Optim., 7(1997), 26-33.
    • (1997) SIAM J. Optim , vol.7 , pp. 26-33
    • Raydan, M.1
  • 24
    • 0036471006 scopus 로고    scopus 로고
    • Relaxed steepest descent and Cauchy -Barzilai-Borwein method
    • M. Raydan and B. F. Svaiter, Relaxed steepest descent and Cauchy -Barzilai-Borwein method, Comp. Optim. Appl. 21(2002), 155-167.
    • (2002) Comp. Optim. Appl , vol.21 , pp. 155-167
    • Raydan, M.1    Svaiter, B.F.2
  • 25
    • 18044401847 scopus 로고    scopus 로고
    • A new matrix-free Algorithm for the largescale trust-region subproblem
    • M. Rojas, S. A. Santos and D. C. Sorensen, A new matrix-free Algorithm for the largescale trust-region subproblem, SIAM J. Optim., Vol.11, No. 3, pp. 611-646.
    • SIAM J. Optim , vol.11 , Issue.3 , pp. 611-646
    • Rojas, M.1    Santos, S.A.2    Sorensen, D.C.3
  • 26
    • 4444343782 scopus 로고    scopus 로고
    • Convergence of line search methods for unconstrained optimization
    • Z. J. Shi, Convergence of line search methods for unconstrained optimization, Applied Mathematics and Computation. 157(2004), 393-405.
    • (2004) Applied Mathematics and Computation , vol.157 , pp. 393-405
    • Shi, Z.J.1
  • 27
    • 0040570969 scopus 로고    scopus 로고
    • A note on minimization problems and multistep methods
    • J. Schropp, A note on minimization problems and multistep methods, Numer. Math., 78(1997), 87-101.
    • (1997) Numer. Math , vol.78 , pp. 87-101
    • Schropp, J.1
  • 28
    • 0034348737 scopus 로고    scopus 로고
    • One-step and multistep procedures for constrained minimization problems
    • J. Schropp, One-step and multistep procedures for constrained minimization problems, IMA J. Numer. Anal., 20(2000), 135-152.
    • (2000) IMA J. Numer. Anal , vol.20 , pp. 135-152
    • Schropp, J.1
  • 29
    • 0022015590 scopus 로고
    • A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties
    • G. A. Schultz, R. B. Schnabel, and R. H. Bryrd, A family of trust-region-based algorithms for unconstrained minimization with strong global convergence properties, SIAM Journal on Numerical Analysis, 22(1985), 47-67.
    • (1985) SIAM Journal on Numerical Analysis , vol.22 , pp. 47-67
    • Schultz, G.A.1    Schnabel, R.B.2    Bryrd, R.H.3
  • 30
    • 0021624184 scopus 로고
    • Differential optimization techniques
    • D. J. Van Wyk, Differential optimization techniques, Appl. Math. Model., 8(1984), 419-424.
    • (1984) Appl. Math. Model , vol.8 , pp. 419-424
    • Van Wyk, D.J.1
  • 31
    • 0022076594 scopus 로고
    • A trust-region algorithm for equality constrained minimization: Convergence properties and implementation
    • A. Vardi, A trust-region algorithm for equality constrained minimization: Convergence properties and implementation, SIAM Journal of Numerical Analysis, 22(1985), 575-579.
    • (1985) SIAM Journal of Numerical Analysis , vol.22 , pp. 575-579
    • Vardi, A.1
  • 32
    • 0033899834 scopus 로고    scopus 로고
    • A class of gradient unconstrained minimization algorithms with adaptive stepsize
    • M. N. Vrahatis, G. S. Androulakis, J. N. Lambrinos and G. D. Magolas, A class of gradient unconstrained minimization algorithms with adaptive stepsize, J. Comput. Appl. Math., 114(2000), 367-386.
    • (2000) J. Comput. Appl. Math , vol.114 , pp. 367-386
    • Vrahatis, M.N.1    Androulakis, G.S.2    Lambrinos, J.N.3    Magolas, G.D.4
  • 33
    • 33645848452 scopus 로고    scopus 로고
    • New quasi-Newton methods for unconstrained optimization problems
    • Z. Wei, G. Li, L. Qi, 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
  • 34
    • 5544237802 scopus 로고    scopus 로고
    • The superlinear convergence of a modified BFGS-type method for unconstrained optimization
    • Z. Wei, G. Yu, G. Yuan and Z. Lian, 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
  • 36
    • 0033164194 scopus 로고    scopus 로고
    • New quasi-Newton equation and related methods for unconstrained optimization
    • J. Zhang, N. Deng, and L. Chen, New quasi-Newton equation and related methods for unconstrained optimization, Journal of Optimization Theory and Applications, Vol. 102, No. 1, 1999, pp. 147-167.
    • (1999) Journal of Optimization Theory and Applications , vol.102 , Issue.1 , pp. 147-167
    • Zhang, J.1    Deng, N.2    Chen, L.3
  • 37
    • 9944262108 scopus 로고    scopus 로고
    • A nonmonotone line search technique and its application to unconstrained optimization
    • H. C. Zhang and W. W. Hager A nonmonotone line search technique and its application to unconstrained optimization, SIAM J. Optim., Vol. 14, No. 4, 2004, pp. 1043-1056.
    • (2004) SIAM J. Optim , vol.14 , Issue.4 , pp. 1043-1056
    • Zhang, H.C.1    Hager, W.W.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.