메뉴 건너뛰기




Volumn 19, Issue 1, 2008, Pages 307-325

A first-order convergence analysis of trust-region methods with inexact Jacobians

Author keywords

Global convergence; Inexact Jacobians; Trust region algorithms

Indexed keywords

CONVERGENCE OF NUMERICAL METHODS; QUADRATIC PROGRAMMING;

EID: 61349174687     PISSN: 10526234     EISSN: None     Source Type: Journal    
DOI: 10.1137/050634530     Document Type: Article
Times cited : (7)

References (29)
  • 1
    • 1942486324 scopus 로고    scopus 로고
    • A trust region SQP algorithm for equality constrained parameter estimation with simple parameter bounds
    • A. ARORA AND L. BIEGLER, A trust region SQP algorithm for equality constrained parameter estimation with simple parameter bounds, Comput. Optim. Appl., 28 (2004), pp. 51-86.
    • (2004) Comput. Optim. Appl , vol.28 , pp. 51-86
    • ARORA, A.1    BIEGLER, L.2
  • 3
    • 61349156065 scopus 로고    scopus 로고
    • Inexact SQP Methods for Equality Constrained Optimization
    • Tech. report, Northwestern University, Evanston, IL
    • R. BYRD, F. CURTIS, AND J. NOCEDAL, Inexact SQP Methods for Equality Constrained Optimization, Tech. report, Northwestern University, Evanston, IL, 2006.
    • (2006)
    • BYRD, R.1    CURTIS, F.2    NOCEDAL, J.3
  • 4
    • 0001130234 scopus 로고    scopus 로고
    • A trust region method based on interior point techniques for nonlinear programming
    • R. BYRD, J. GILBERT, AND J. NOCEDAL, A trust region method based on interior point techniques for nonlinear programming, Math. Program., 89A (2000), pp. 149-185.
    • (2000) Math. Program , vol.89 A , pp. 149-185
    • BYRD, R.1    GILBERT, J.2    NOCEDAL, J.3
  • 5
    • 0002336672 scopus 로고
    • A trust region strategy for nonlinear equality constrained optimization
    • P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds, SIAM, Philadelphia
    • M. CELIS, J. DENNIS, AND R. TAPIA, A trust region strategy for nonlinear equality constrained optimization, in Numerical Optimization, 1984, P. T. Boggs, R. H. Byrd, and R. B. Schnabel, eds., SIAM, Philadelphia, 1985.
    • (1985) Numerical Optimization, 1984
    • CELIS, M.1    DENNIS, J.2    TAPIA, R.3
  • 6
    • 33845521414 scopus 로고
    • Convergence of quasi-Newton matrices generated by the symmetric rank one update
    • A. CONN, N. GOULD, AND P. TOINT, Convergence of quasi-Newton matrices generated by the symmetric rank one update, Math. Program., 50A (1991), pp. 177-196.
    • (1991) Math. Program , vol.50 A , pp. 177-196
    • CONN, A.1    GOULD, N.2    TOINT, P.3
  • 8
    • 0031542597 scopus 로고    scopus 로고
    • A global convergence theory for general trust-region-based algorithms for equality constrained optimization
    • J. DENNIS, M. EL-ALEM, AND M. MACIEL, A global convergence theory for general trust-region-based algorithms for equality constrained optimization, SIAM J. Optim., 7 (1997), pp. 177-207.
    • (1997) SIAM J. Optim , vol.7 , pp. 177-207
    • DENNIS, J.1    EL-ALEM, M.2    MACIEL, M.3
  • 9
    • 0026104343 scopus 로고
    • A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization
    • M. EL-ALEM, A global convergence theory for the Celis-Dennis-Tapia trust-region algorithm for constrained optimization, SIAM J. Numer. Anal., 28 (1991), pp. 266-290.
    • (1991) SIAM J. Numer. Anal , vol.28 , pp. 266-290
    • EL-ALEM, M.1
  • 10
    • 0042354662 scopus 로고    scopus 로고
    • Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming
    • R. FLETCHER, N. GOULD, S. LEYFFER, P. TOINT, AND A. WÄCHTER, Global convergence of a trust-region SQP-filter algorithm for general nonlinear programming, SIAM J. Optim., 13 (2003), pp. 635-659.
    • (2003) SIAM J. Optim , vol.13 , pp. 635-659
    • FLETCHER, R.1    GOULD, N.2    LEYFFER, S.3    TOINT, P.4    WÄCHTER, A.5
  • 11
    • 0001556338 scopus 로고    scopus 로고
    • Nonlinear programming without a penalty function
    • R. FLETCHER AND S. LEYFFER, Nonlinear programming without a penalty function, Math. Program., 91A (2002), pp. 239-269.
    • (2002) Math. Program , vol.91 A , pp. 239-269
    • FLETCHER, R.1    LEYFFER, S.2
  • 12
    • 0037288670 scopus 로고    scopus 로고
    • On the global convergence of a filter-SQP algorithm
    • R. FLETCHER, S. LEYFFER, AND P. TOINT, On the global convergence of a filter-SQP algorithm, SIAM J. Optim., 13 (2002), pp. 44-59.
    • (2002) SIAM J. Optim , vol.13 , pp. 44-59
    • FLETCHER, R.1    LEYFFER, S.2    TOINT, P.3
  • 13
    • 0000480619 scopus 로고    scopus 로고
    • Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters
    • F. GOMES, M. MACIEL, AND J. MARTINEZ, Nonlinear programming algorithms using trust regions and augmented Lagrangians with nonmonotone penalty parameters, Math. Program., 84A (1999), pp. 161-200.
    • (1999) Math. Program , vol.84 A , pp. 161-200
    • GOMES, F.1    MACIEL, M.2    MARTINEZ, J.3
  • 15
    • 0036817650 scopus 로고    scopus 로고
    • On constrained optimization by adjoint-based quasi-Newton methods
    • A. GRIEWANK AND A. WALTHER, On constrained optimization by adjoint-based quasi-Newton methods, Optim. Methods Softw., 17 (2002), pp. 869-889.
    • (2002) Optim. Methods Softw , vol.17 , pp. 869-889
    • GRIEWANK, A.1    WALTHER, A.2
  • 16
    • 33847293310 scopus 로고    scopus 로고
    • Maintaining factorized KKT systems subject to rank-one updates of Hessians and Jacobians
    • A. GRIEWANK, A. WALTHER, AND M. KORZEC, Maintaining factorized KKT systems subject to rank-one updates of Hessians and Jacobians, Optim. Methods Softw., 22 (2007), pp. 279-295.
    • (2007) Optim. Methods Softw , vol.22 , pp. 279-295
    • GRIEWANK, A.1    WALTHER, A.2    KORZEC, M.3
  • 17
    • 0036013022 scopus 로고    scopus 로고
    • Analysis of inexact trust-region SQP algorithms
    • M. HEINKENSCHLOSS AND L. VICENTE, Analysis of inexact trust-region SQP algorithms, SIAM J. Optim., 12 (2001), pp. 283-302.
    • (2001) SIAM J. Optim , vol.12 , pp. 283-302
    • HEINKENSCHLOSS, M.1    VICENTE, L.2
  • 18
    • 0030679170 scopus 로고    scopus 로고
    • Global convergence of inexact reduced SQP methods
    • H. JÄGER AND E. SACHS, Global convergence of inexact reduced SQP methods, Optim. Methods Softw., 7 (1997), pp. 83-110.
    • (1997) Optim. Methods Softw , vol.7 , pp. 83-110
    • JÄGER, H.1    SACHS, E.2
  • 19
    • 0038286510 scopus 로고    scopus 로고
    • Optimization of pressure swing adsorption systems for air separation
    • L. JIANG, L. BIEGLER, AND G. FOX, Optimization of pressure swing adsorption systems for air separation, AIChE J., 49 (2003), pp. 1140-1157.
    • (2003) AIChE J , vol.49 , pp. 1140-1157
    • JIANG, L.1    BIEGLER, L.2    FOX, G.3
  • 20
    • 0032327604 scopus 로고    scopus 로고
    • On the implementation of an algorithm for large-scale equality constrained optimization
    • M. LALEE, J. NOCEDAL, AND T. PLANTENGA, On the implementation of an algorithm for large-scale equality constrained optimization, SIAM J. Optim., 8 (1998), pp. 682-706.
    • (1998) SIAM J. Optim , vol.8 , pp. 682-706
    • LALEE, M.1    NOCEDAL, J.2    PLANTENGA, T.3
  • 21
    • 0343192198 scopus 로고    scopus 로고
    • Inexact SQP interior point methods and large scale optimal control problems
    • F. LEIBFRITZ AND E. SACHS, Inexact SQP interior point methods and large scale optimal control problems, SIAM J. Control Optim., 38 (1999), pp. 272-293.
    • (1999) SIAM J. Control Optim , vol.38 , pp. 272-293
    • LEIBFRITZ, F.1    SACHS, E.2
  • 24
    • 0025540157 scopus 로고
    • A trust region algorithm for equality constrained optimization
    • M. POWELL AND Y. YUAN, A trust region algorithm for equality constrained optimization, Math. Program., 49A (1990), pp. 189-211.
    • (1990) Math. Program , vol.49 A , pp. 189-211
    • POWELL, M.1    YUAN, Y.2
  • 25
    • 0022015590 scopus 로고
    • A family of trust region based algorithms for unconstrained minimization with strong global convergence properties
    • G. SHULTZ, R. SCHNABEL, AND R. BYRD, A family of trust region based algorithms for unconstrained minimization with strong global convergence properties, SIAM J. Numer. Anal., 22 (1985), pp. 47-67.
    • (1985) SIAM J. Numer. Anal , vol.22 , pp. 47-67
    • SHULTZ, G.1    SCHNABEL, R.2    BYRD, R.3
  • 26
    • 21044440965 scopus 로고    scopus 로고
    • Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function
    • M. ULBRICH AND S. ULBRICH, Non-monotone trust region methods for nonlinear equality constrained optimization without a penalty function, Math. Program., 95B (2003), pp. 103-135.
    • (2003) Math. Program , vol.95 B , pp. 103-135
    • ULBRICH, M.1    ULBRICH, S.2
  • 27
    • 0037860830 scopus 로고    scopus 로고
    • Affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods
    • S. VOLKWEIN AND M. WEISER, Affine invariant convergence analysis for inexact augmented Lagrangian-SQP methods, SIAM J. Control Optim., 41 (2002), pp. 875-899.
    • (2002) SIAM J. Control Optim , vol.41 , pp. 875-899
    • VOLKWEIN, S.1    WEISER, M.2
  • 28
    • 61349192196 scopus 로고    scopus 로고
    • A. WALTHER AND L. BIEGLER, A Trust-Region Algorithm for Nonlinear Programming Problems with Dense Constraint Jacobians, Tech. report MATH-WR-01-2007, TU Dresden, submitted.
    • A. WALTHER AND L. BIEGLER, A Trust-Region Algorithm for Nonlinear Programming Problems with Dense Constraint Jacobians, Tech. report MATH-WR-01-2007, TU Dresden, submitted.
  • 29
    • 2642568903 scopus 로고    scopus 로고
    • KNITRO User's Manual
    • 05/2003, Optimization Technology Center, Northwestern University, Evanston, IL
    • R. WALTZ AND J. NOCEDAL, KNITRO User's Manual, Tech. report OTC 05/2003, Optimization Technology Center, Northwestern University, Evanston, IL, 2003.
    • (2003) Tech. report OTC
    • WALTZ, R.1    NOCEDAL, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.