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Volumn 30, Issue 3, 2015, Pages 478-491

On the modified trust region algorithm for nonlinear equations

Author keywords

local error bound condition; modified trust region method; nonlinear equations

Indexed keywords

OPTIMIZATION; SOFTWARE ENGINEERING;

EID: 84933673710     PISSN: 10556788     EISSN: 10294937     Source Type: Journal    
DOI: 10.1080/10556788.2014.932943     Document Type: Article
Times cited : (8)

References (27)
  • 3
    • 33745178146 scopus 로고    scopus 로고
    • Convergence rate of the trust region method for nonlinear equations under local error bound condition
    • J.Y. Fan, Convergence rate of the trust region method for nonlinear equations under local error bound condition, Comput. Optim. Appl. 34 (2006), pp. 215-227.
    • (2006) Comput. Optim. Appl. , vol.34 , pp. 215-227
    • Fan, J.Y.1
  • 4
    • 84858953433 scopus 로고    scopus 로고
    • The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence
    • J.Y. Fan, The modified Levenberg-Marquardt method for nonlinear equations with cubic convergence, Math. Comput. 81 (2012), pp. 447-466.
    • (2012) Math. Comput. , vol.81 , pp. 447-466
    • Fan, J.Y.1
  • 5
    • 78649519019 scopus 로고    scopus 로고
    • A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius
    • J.Y. Fan and J.Y. Pan, A modified trust region algorithm for nonlinear equations with new updating rule of trust region radius, Int. J. Comput. Math. 87 (2010), pp. 3186-3195.
    • (2010) Int. J. Comput. Math. , vol.87 , pp. 3186-3195
    • Fan, J.Y.1    Pan, J.Y.2
  • 6
    • 79951683200 scopus 로고    scopus 로고
    • An improved trust region algorithm for nonlinear equations
    • J.Y. Fan and J.Y. Pan, An improved trust region algorithm for nonlinear equations, Comput. Optim. Appl. 48 (2011), pp. 59-70.
    • (2011) Comput. Optim. Appl. , vol.48 , pp. 59-70
    • Fan, J.Y.1    Pan, J.Y.2
  • 8
    • 13744251115 scopus 로고    scopus 로고
    • On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption
    • J.Y. Fan and Y.X. Yuan, On the quadratic convergence of the Levenberg-Marquardt method without nonsingularity assumption, Computing 74 (2005), pp. 23-39.
    • (2005) Computing , vol.74 , pp. 23-39
    • Fan, J.Y.1    Yuan, Y.X.2
  • 9
    • 0002914778 scopus 로고
    • Iterative Methods for Linear and Nonlinear Equations
    • SIAM, Philadelphia, PA
    • C.T. Kelley, Iterative Methods for Linear and Nonlinear Equations, Frontiers in Applied Mathematics 16, SIAM, Philadelphia, PA, 1995.
    • (1995) Frontiers in Applied Mathematics , vol.16
    • Kelley, C.T.1
  • 10
    • 3242678233 scopus 로고    scopus 로고
    • Solving Nonlinear Equations with Newton's Method
    • SIAM, Philadelphia, PA
    • C.T. Kelley, Solving Nonlinear Equations with Newton's Method, Fundamentals of Algorithms, SIAM, Philadelphia, PA, 2003.
    • (2003) Fundamentals of Algorithms
    • Kelley, C.T.1
  • 11
    • 0000873069 scopus 로고
    • A method for the solution of certain nonlinear problems in least squares
    • K. Levenberg, A method for the solution of certain nonlinear problems in least squares, Quart. Appl. Math. 2 (1944), pp. 164-166.
    • (1944) Quart. Appl. Math. , vol.2 , pp. 164-166
    • Levenberg, K.1
  • 12
    • 0035730349 scopus 로고    scopus 로고
    • Globally convergent Broyden-like methods for semismooth equations and applications to VIP, NCP, MCP
    • D.H. Li and M. Fukushima, Globally convergent Broyden-like methods for semismooth equations and applications to VIP, NCP, MCP, Ann. Oper. Res. 102 (2001), pp. 71-97.
    • (2001) Ann. Oper. Res. , vol.102 , pp. 71-97
    • Li, D.H.1    Fukushima, M.2
  • 13
    • 0000169232 scopus 로고
    • An algorithm for least-squares estimation of nonlinear inequalities
    • D.W. Marquardt, An algorithm for least-squares estimation of nonlinear inequalities, SIAM J. Appl. Math. 11 (1963), pp. 431-441.
    • (1963) SIAM J. Appl. Math. , vol.11 , pp. 431-441
    • Marquardt, D.W.1
  • 14
    • 0001056223 scopus 로고
    • A methodology for solving chemical equilibrium system
    • K. Meintjes and A.P. Morgan, A methodology for solving chemical equilibrium system, Appl. Math. Comput. 22 (1987), pp. 333-361.
    • (1987) Appl. Math. Comput. , vol.22 , pp. 333-361
    • Meintjes, K.1    Morgan, A.P.2
  • 15
    • 0025448634 scopus 로고
    • Chemical equilibrium systems as numerical test problems
    • K. Meintjes and A.P. Morgan, Chemical equilibrium systems as numerical test problems, ACM Trans. Math. Softw. 16 (1990), pp. 143-151.
    • (1990) ACM Trans. Math. Softw. , vol.16 , pp. 143-151
    • Meintjes, K.1    Morgan, A.P.2
  • 17
    • 0002468725 scopus 로고    scopus 로고
    • Combining trust region and line search techniques
    • Y. Yuan, ed. Kluwer, Dordrecht
    • J. Nocedal and Y.X. Yuan, Combining trust region and line search techniques, in Advances in Nonlinear Programming, Y. Yuan, ed., Kluwer, Dordrecht, 1998, pp. 153-175.
    • (1998) Advances in Nonlinear Programming , pp. 153-175
    • Nocedal, J.1    Yuan, Y.X.2
  • 19
    • 0002302301 scopus 로고
    • Convergence properties of a class of minimization algorithms
    • O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds. Academic Press, New York
    • M.J.D. Powell, Convergence properties of a class of minimization algorithms, in Nonlinear Programming 2, O.L. Mangasarian, R.R. Meyer and S.M. Robinson, eds., Academic Press, New York, 1975, pp. 1-27.
    • (1975) Nonlinear Programming , vol.2 , pp. 1-27
    • Powell, M.J.D.1
  • 20
    • 0021510543 scopus 로고
    • Tensor methods for nonlinear equations
    • R.B. Schnabel and P.D. Frank, Tensor methods for nonlinear equations, SIAM J. Numer. Anal. 21 (1984), pp. 815-843.
    • (1984) SIAM J. Numer. Anal. , vol.21 , pp. 815-843
    • Schnabel, R.B.1    Frank, P.D.2
  • 21
    • 27144516174 scopus 로고    scopus 로고
    • A composite third order Newton-Steffensen method for solving nonlinear equations
    • J.R. Sharma, A composite third order Newton-Steffensen method for solving nonlinear equations, Appl. Math. Comput. 169 (2005), pp. 242-246.
    • (2005) Appl. Math. Comput. , vol.169 , pp. 242-246
    • Sharma, J.R.1
  • 22
    • 0002621771 scopus 로고    scopus 로고
    • Error bounds and superlinear convergence analysis of some Newton-type methods in optimization
    • Kluwer Academic Publishers, Dordrecht
    • P. Tseng, Error bounds and superlinear convergence analysis of some Newton-type methods in optimization, in Nonlinear Optimization and Applications 2, Kluwer Academic Publishers, Dordrecht, 1998.
    • (1998) Nonlinear Optimization and Applications , vol.2
    • Tseng, P.1
  • 24
    • 0011662308 scopus 로고    scopus 로고
    • On the rate of convergence of the Levenberg-Marquardt method
    • N. Yamashita and M. Fukushima, On the rate of convergence of the Levenberg-Marquardt method, Computing (Supplement 15), (2001), pp. 237-249.
    • (2001) Computing , pp. 237-249
    • Yamashita, N.1    Fukushima, M.2
  • 25
    • 0013230184 scopus 로고    scopus 로고
    • Trust region algorithms for nonlinear equations
    • Y.X. Yuan, Trust region algorithms for nonlinear equations, Information 1 (1998), pp. 7-20.
    • (1998) Information , vol.1 , pp. 7-20
    • Yuan, Y.X.1
  • 26
    • 84875274284 scopus 로고    scopus 로고
    • Recent advances in numerical methods for nonlinear equations and nonlinear least squares
    • Y.X. Yuan, Recent advances in numerical methods for nonlinear equations and nonlinear least squares, Numer. Algebra Control Optim. 1 (2011), pp. 15-34.
    • (2011) Numer. Algebra Control Optim. , vol.1 , pp. 15-34
    • Yuan, Y.X.1
  • 27
    • 21144457822 scopus 로고    scopus 로고
    • A new trust region method for nonlinear equations
    • J.L. Zhang and Y. Wang, A new trust region method for nonlinear equations, Math. Meth. Oper. Res. 58 (2003), pp. 283-298.
    • (2003) Math. Meth. Oper. Res. , vol.58 , pp. 283-298
    • Zhang, J.L.1    Wang, Y.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.