메뉴 건너뛰기




Volumn 115, Issue 2, 2008, Pages 199-222

A local convergence property of primal-dual methods for nonlinear programming

Author keywords

Barrier methods; Constrained optimization; Interior point methods; Nonlinear programming; Primal dual methods

Indexed keywords

AEROSPACE APPLICATIONS; COMPUTER NETWORKS; DYNAMIC PROGRAMMING; LINEAR PROGRAMMING; MATHEMATICAL PROGRAMMING; NEWTON-RAPHSON METHOD; NONLINEAR PROGRAMMING; PERTURBATION TECHNIQUES; STANDARDS;

EID: 45149089405     PISSN: 00255610     EISSN: 14364646     Source Type: Journal    
DOI: 10.1007/s10107-007-0136-2     Document Type: Article
Times cited : (11)

References (23)
  • 1
    • 45149130859 scopus 로고    scopus 로고
    • Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming
    • to appear
    • Armand, P., Benoist, J., Orban, D.: Dynamic updates of the barrier parameter in primal-dual methods for nonlinear programming. Comput. Optim. Appl. (2007)(to appear)
    • (2007) Comput. Optim. Appl.
    • Armand, P.1    Benoist, J.2    Orban, D.3
  • 2
    • 0012691880 scopus 로고    scopus 로고
    • On the local behaviour of an interior point method for nonlinear programming
    • Addison-Welsey Harlow
    • Byrd R.H., Liu G. and Nocedal J. (1997). On the local behaviour of an interior point method for nonlinear programming. In: Griffiths, D.F., Higham, D.J., and Watson, G.A. (eds) Numerical Analysis 1997., pp 37-56. Addison-Welsey, Harlow
    • (1997) Numerical Analysis 1997. , pp. 37-56
    • Byrd, R.H.1    Liu, G.2    Nocedal, J.3    Griffiths, D.F.4    Higham, D.J.5    Watson, G.A.6
  • 3
    • 34249771074 scopus 로고
    • On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds
    • Coleman T.F. and Li Y. (1994). On the convergence of interior-reflective Newton methods for nonlinear minimization subject to bounds. Math. Prog. 67: 189-224
    • (1994) Math. Prog. , vol.67 , pp. 189-224
    • Coleman, T.F.1    Li, Y.2
  • 4
    • 0000134828 scopus 로고
    • Numerical stability and efficiency of penalty algorithms
    • Dussault J.P. (1995). Numerical stability and efficiency of penalty algorithms. SIAM J. Numer. Anal. 32: 296-317
    • (1995) SIAM J. Numer. Anal. , vol.32 , pp. 296-317
    • Dussault, J.P.1
  • 5
    • 0035302991 scopus 로고    scopus 로고
    • On the superlinear convergence order of the logarithmic barrier algorithm
    • Dussault J.P. and Elafia A. (2001). On the superlinear convergence order of the logarithmic barrier algorithm. Comput. Optim. Appl. 19: 31-53
    • (2001) Comput. Optim. Appl. , vol.19 , pp. 31-53
    • Dussault, J.P.1    Elafia, A.2
  • 6
    • 0030541525 scopus 로고    scopus 로고
    • On the formulation and theory of the Newton interior-point method for nonlinear programming
    • El-Bakry A.S., Tapia R.A., Tsuchiya T. and Zhang Y. (1996). On the formulation and theory of the Newton interior-point method for nonlinear programming. J. Optim. Theory Appl. 89: 507-541
    • (1996) J. Optim. Theory Appl. , vol.89 , pp. 507-541
    • El-Bakry, A.S.1    Tapia, R.A.2    Tsuchiya, T.3    Zhang, Y.4
  • 9
    • 0035603909 scopus 로고    scopus 로고
    • Superlinear convergence of primal-dual interior point algorithms for nonlinear programming
    • Gould N.I.M., Orban D., Sartenaer A. and Toint P.L. (2001). Superlinear convergence of primal-dual interior point algorithms for nonlinear programming. SIAM J. Optim. 11: 974-1002
    • (2001) SIAM J. Optim. , vol.11 , pp. 974-1002
    • Gould, N.I.M.1    Orban, D.2    Sartenaer, A.3    Toint, P.L.4
  • 10
    • 21044436557 scopus 로고    scopus 로고
    • Componentwise fast convergence in the solution of full-rank systems of nonlinear equations
    • Gould N.I.M., Orban D., Sartenaer A. and Toint P.L. (2002). Componentwise fast convergence in the solution of full-rank systems of nonlinear equations. Math. Prog. 92: 481-508
    • (2002) Math. Prog. , vol.92 , pp. 481-508
    • Gould, N.I.M.1    Orban, D.2    Sartenaer, A.3    Toint, P.L.4
  • 11
    • 0000860416 scopus 로고    scopus 로고
    • Superlinear and quadratic convergence of affine- scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption
    • Heinkenschloss M., Ulbrich M. and Ulbrich S. (1999). Superlinear and quadratic convergence of affine- scaling interior-point Newton methods for problems with simple bounds without strict complementarity assumption. Math. Prog. 86: 615-635
    • (1999) Math. Prog. , vol.86 , pp. 615-635
    • Heinkenschloss, M.1    Ulbrich, M.2    Ulbrich, S.3
  • 12
    • 0007294939 scopus 로고
    • On the characterization of Q-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming
    • Martinez H.J., Parada Z. and Tapia R.A. (1995). On the characterization of Q-superlinear convergence of quasi-Newton interior-point methods for nonlinear programming. Bol. Soc. Mat. Mexicana 1: 137-148
    • (1995) Bol. Soc. Mat. Mexicana , vol.1 , pp. 137-148
    • Martinez, H.J.1    Parada, Z.2    Tapia, R.A.3
  • 14
    • 1542291020 scopus 로고    scopus 로고
    • A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties
    • Tits A.L., Wächter A., Bakhtiari S., Urban T.J. and Lawrence C.T. (2003). A primal-dual interior-point method for nonlinear programming with strong global and local convergence properties. SIAM J. Optim. 14: 173-199
    • (2003) SIAM J. Optim. , vol.14 , pp. 173-199
    • Tits, A.L.1    Wächter, A.2    Bakhtiari, S.3    Urban, T.J.4    Lawrence, C.T.5
  • 15
    • 14944387007 scopus 로고    scopus 로고
    • A globally convergent primal-dual interior-point filter method for nonlinear programming
    • Ulbrich M., Ulbrich S. and Vicente L.N. (2004). A globally convergent primal-dual interior-point filter method for nonlinear programming. Math. Prog. 100: 379-410
    • (2004) Math. Prog. , vol.100 , pp. 379-410
    • Ulbrich, M.1    Ulbrich, S.2    Vicente, L.N.3
  • 16
    • 0000287204 scopus 로고    scopus 로고
    • An interior-point algorithm for nonconvex nonlinear programming
    • Vanderbei R.J. and Shanno D.F. (1999). An interior-point algorithm for nonconvex nonlinear programming. Comput. Optim. Appl. 13: 231-252
    • (1999) Comput. Optim. Appl. , vol.13 , pp. 231-252
    • Vanderbei, R.J.1    Shanno, D.F.2
  • 17
    • 0034293909 scopus 로고    scopus 로고
    • Local convergence of the affine-scaling interior-point algorithm for nonlinear programming
    • Vicente L.N. (2000). Local convergence of the affine-scaling interior-point algorithm for nonlinear programming. Comput. Optim. Appl. 17: 23-35
    • (2000) Comput. Optim. Appl. , vol.17 , pp. 23-35
    • Vicente, L.N.1
  • 18
    • 0036737815 scopus 로고    scopus 로고
    • Local convergence of a primal-dual method for degenerate nonlinear programming
    • Vicente L.N. and Wright S.J. (2002). Local convergence of a primal-dual method for degenerate nonlinear programming. Comput. Optim. Appl. 22: 311-328
    • (2002) Comput. Optim. Appl. , vol.22 , pp. 311-328
    • Vicente, L.N.1    Wright, S.J.2
  • 19
    • 29144523061 scopus 로고    scopus 로고
    • On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
    • Wächter A. and Biegler L.T. (2006). On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math. Prog. 106: 25-57
    • (2006) Math. Prog. , vol.106 , pp. 25-57
    • Wächter, A.1    Biegler, L.T.2
  • 20
    • 33645294357 scopus 로고    scopus 로고
    • An interior algorithm for nonlinear optimization that combines line search and trust region steps
    • Waltz R.A., Morales J.L., Nocedal J. and Orban D. (2006). An interior algorithm for nonlinear optimization that combines line search and trust region steps. Math. Prog. 107: 391-408
    • (2006) Math. Prog. , vol.107 , pp. 391-408
    • Waltz, R.A.1    Morales, J.L.2    Nocedal, J.3    Orban, D.4
  • 21
    • 0010908414 scopus 로고    scopus 로고
    • Q-superlinear convergence of primal-dual interior point quasi-Newton methods for constrained optimization
    • Yabe H. and Yamashita H. (1997). Q-superlinear convergence of primal-dual interior point quasi-Newton methods for constrained optimization. J. Oper. Res. Soc. Jpn 40: 415-436
    • (1997) J. Oper. Res. Soc. Jpn , vol.40 , pp. 415-436
    • Yabe, H.1    Yamashita, H.2
  • 22
    • 0000273506 scopus 로고    scopus 로고
    • Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization
    • Yamashita H. and Yabe H. (1996). Superlinear and quadratic convergence of some primal-dual interior point methods for constrained optimization. Math. Prog. 75: 377-397
    • (1996) Math. Prog. , vol.75 , pp. 377-397
    • Yamashita, H.1    Yabe, H.2
  • 23
    • 12344256897 scopus 로고    scopus 로고
    • A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization
    • Yamashita H., Yabe H. and Tanabe T. (2005). A globally and superlinearly convergent primal-dual interior point trust region method for large scale constrained optimization. Math. Prog. 102: 111-151
    • (2005) Math. Prog. , vol.102 , pp. 111-151
    • Yamashita, H.1    Yabe, H.2    Tanabe, T.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.